I would challenge the assumption that the evils committed while a person is alive are finite.

Presumably, you are suggesting this because they took place during a finite period of time, or because human capability is finite. However, the duration of the evil is not the (only) way to determine the "magnitude" of the evil. If one reasonable definition of "evil" is "that which is not good", then the amount of evil would be related to how far away from good it is.

Under the Christian belief system, the standard of "good" is God; who is considered "infinitely good", or "perfect". Something which less than infinite is not finitely less than the infinite. In other words, the scale is not 1-10, where if you get a 2 it means that you were "level 8 evil; 8 short of perfect". Rather, the scale is 1-infinity, where getting a 2 means that you were infinitely evil. Even getting a 1,000,000 is still "infinitely evil".

This general reasoning is explained by J. Warner Wallace, along with a few other explanations, in this article on coldcasechristianity:

If someone embezzles $5.00 a week from their employer’s cash register they will have stolen $260.00 over the course of a year. If they’re caught at the end of this time, they would still only be guilty of a misdemeanor in the State of California (based on the total amount of loss). Although the crime took a year to commit, the perpetrator wouldn’t spend much (if any) time in jail. On the other hand, a murder can take place in the blink of an eye and the resulting punishment will be life in prison (or perhaps the death penalty). The duration of the crime clearly has little or nothing to do with the duration of the penalty.

And

Finally, it’s important to remember the nature of the crime that eventually leads one to Hell. It’s not the fact you kicked your dog in 1992. It’s not the fact you had evil thoughts about your teacher in 1983. The crime that earns us a place in Hell is our rejection of the true, living, eternal God. The rejection of God’s forgiveness is not finite. People who reject Jesus have rejected Him completely. They have rejected Him as an ultimate, final mortal decision. God has the right (and obligation) to judge them with an appropriate punishment. To argue that God’s punishment does not fit our crime is to underestimate our crime.

As a member of the Church of Jesus Christ of Latter-day Saints the view is different.

God is Just. Satan's greatest lie is that you can get away with something. God is absolutely just and you will pay back everyone you hurt in this life and will be accountable for every action and every thought.

Jesus and the atonement brings mercy for those who sincerely seek it and have done everything in their power to make things right. Christ and his atonement cleans up all the residual (good not done and ripples that spread out throughout mankind from each wrong act).

Hell is each person paying back those they hurt. And the consequences of ignoring their conscience (God's voice in your soul) in this life.

As in the book, "Heaven and Hell" by EMANUEL SWEDENBORG 1700s (not LDS) the top heaven is for those who love God (the $500,000,000,000 reward). The second kingdom is for those who love others (the $1,000,000,000 reward). The third kingdom is for those who who love themselves ($1,000,000 reward). A loving God wants to bless ALL his children and we each choose how much we will receive at his hands. No one is assigned to a kingdom until they have completed their "hell". You pay everyone back, make everything right, grow as you needed to and go on to your reward. Even the worst of us will be blessed for having this earth life.

The Doctrine and Covenants 19:4-19 explains that since God is endless, punishment at his hands is endless punishment but it does not last forever, just until we pay the price for our sins (sin being anything that keeps us from becoming our best self).

So, Mercy claims those who ask for it through turning to Jesus Christ and giving yourself to him and Justice is what everyone else gets. God who loves us will bless us each with as much as we are willing to accept. God remains both a merciful and just god committed to our growth and development.

"This is my work and my glory to bring to pass the immortality and eternal life of man." Moses 1:39

In many religions, for example, the Abrahamic ones, there exists a
place of eternal punishment for those who live in violation of God's
commandments. Assuming an infinitely-long afterlife, in which
"sinners" are punished with all the punishments deemed appropriate
that Hell has to offer... doesn't that make God commit more evil than
good by allowing those sinners to experience Hell?

It depends on how you define and measure evil and good. In particular, the answer is a clear "no" in any belief system that views its God as the standard of goodness, or in any in which good and evil are only recognized as characterizing human actions.

Surely, whatever
evils committed while the person in question is alive are finite,

Are they? The duration of any evil acts a person commits in their lifetime is certainly finite, but even from a human perspective, duration is a poor measure of evil. What about the consequences that follow from evil actions? Should not the nature, scope, and duration of those be considered? And if we posit a created universe then we can imagine that there might be consequences even outside the universe, and who can say whether our concept of finiteness even has any meaningfulness there?

while, as (to my understanding) the punishments suffered in Hell are
infinite.

Are they? Suppose Hell is outside the created universe that we have posited, which makes a lot more sense to me than it being inside the universe as I normally mean that term. How do you measure the punishment? Can you even be confident that we have any concepts that would be applicable to measuring?

Note, that this question assumes that God is able to stop the
existence of Hell and the infinite punishment of evil committed by any
man. Thus, making him evil by exerting infinite amounts of suffering
to the sinners by inaction.

Well of course you can reach your desired conclusion by assumption, or by making enough assumptions and definitions of your own choosing to support it. The result of such an effort is contingent on the validity of the assumptions and shaped by the definitions of the terms in which the argument is expressed. It is a useless exercise if those you are trying to persuade disagree with you about your premises.

I can direct you to a quote that provides an answer, from the controversial theologian Thomas Altizer. He basically says that, in the round, the evil created in creation is extinguised in redemption -- signified by the crucifixion. However, there are subtleties as to what he means by 'in the round', i.e. predestination, or viewing the subject as a conceptual whole.

From Godhead and the Nothing, Chapter 5. Evil and the Godhead (page 65)

Why is there any being at all? Why far rather not nothing? This deep
question of Leibnitz was profoundly renewed in the twentieth century,
and asked as it never could have been asked in the seventeenth
century. This becomes perhaps the most ultimate question of Heidegger,
and is just as profoundly asked by Kafka or Beckett, and if this
question is now unanswerable, then so, too, is every ultimate
question. Of course, predestination can answer this question, but if
predestination has now become unthinkable, then so likewise have
Godhead and evil become unthinkable, and above all unthinkable if they
cannot be thought simultaneously and at once. Is it because we cannot
now think Godhead or totality without thinking evil that we so
resolutely refuse to think about God? ... Is damnation the necessarily
unspoken answer to our question as to why is there any being at all?
And if predestination knows the necessity of damnation, and the
absolute necessity of damnation, is that a damnation truly and finally
inseparable from the only redemption that predestination can know?
Here, if "being" is embodied in redemption, must "being" be embodied
in damnation as well?

Of course, it has now become impossible for us truly or actually to
speak of "being," but we have no less lost the capacity to speak of
either damnation or redemption. While this is certainly not true of
full modernity, it is apparently true of a new postmodernity, and
certainly true of a language in which the "I" or the center of
consciousness is silent and unspeakable. Nietzsche could know that "I"
as a pure negativity, an "I" that is the consequence of ressentiment,
but that knowledge is a dialectical knowledge, for it is the
consequence of the full advent of an absolute Yes-saying, a Yes-saying
which Nietzsche knew as redemption. Just as this "I" is a truly evil
"I," one that is the consequence of a pure No-saying, it is this very
"I" that is transfigured in an absolute Yes-saying, and transfigured
by undergoing an ultimate and final reversal, a reversal in which it
becomes the very opposite of itself.

Start finding the word "Hell" in the Bible. Some translations may have it as an interpretation, but if you follow the sources strictly enough you won't find it.
You'll find "Sheol" as a resting place. You'll find "Gehenna" as a valley that in old times were an offering place for gods like Molog and Baal and ended up as a garbage pile. And you'll occasionally find Tartarus as a place for the fallen angels. But not Hell.

It's widely argued the concept of "Heaven" and "Hell" wasn't invented until early Christian and Roman faith intermixed, as a "Christian" take of the roman "Hades". All you can find in earlier literature is reference to places like "Sheol" and Jesus, in one single discussion, making a parable about a servant ending up in "Abrahams bosom" when his rather frugal master did not. When Jesus made a lot of parables and it's doubtful how literally they can be taken.

What you can find is Paul and other early disciples fighting for the idea of being woken up to a new life. Not an ethereal one but material, with new bodies. That death from this life is not final, and that the ones God choose to trust will be given new bodies that won't die.

You'll find this being extensively discussed in the Book of Revelation, but the topic is mentioned here and there during the whole Bible. It's an evolving story, all the way from the fall of Adam and Eve.

There's been a renewed focus on this in later years, because sure enough, the idea of heaven and hell is not ethically defensible. If you want to defend Christian faith you'll have to find something better and stronger. and that's when you begin to read your Bible with new eyes.

When it comes to God's wrath, I like how N.T. Wright described it: "God hates sin in the same way a violin maker would hate to see one of his beautiful creations used as a tennis racquet." Sin is to behave in a way that would long term harm your and/or others, it's originally an archer's term that means to "miss the mark". Do you behave in a way that really works towards the goals you want in your life, or do you not?
The sad thing is, this has all been used to control other people instead of helping them grow, which according to the Bible will meet final judgement one day and surely will be regarded as sin. Paul. for one, warned against behavior that would make people revolt, and this is exactly that kind of behavior.

The closest to this in the bible (I can't comment on any other source from Islam for example) is the lake of fire, which the devil, the beast and his accomplices will be cast into after the 1000 year period where he is let loose upon the world. It is used four times in revelations, two of those times it talks about the devil, the beast and his accomplices, together with the false prophet they will be thrown into the lake, and only one of those times speak about being there forever. The other two times it adds those that are not in the book of life, and it is also added in these two cases that it is referred to as the second death.

It's possible that the eternal suffering and the second death refers to the same thing or two different events. And it's not sure which is meant literally. Because it says suffering forever and ever one place, and second death (which sounds like ceasing to exist).

On the question of whether the existence of the lake of fire makes Him evil, fundamentally goes against the idea of the lake in the first place. It is a just punishment for sins, and God's mercy and grace, sending Christ to die for the world is what makes it possible for us to forgo that just punishment. Rejecting that love is not on Him. And the existence of just punishment does not make him evil.

In the beginning, God created the heavens and the earth. Gen 1:1. Nowhere in the Bible is it stated that God created Hell. God has always allowed man choice. To listen and obey his requirements, or not. Man was given eternal life, and death was mentioned ONLY if disobedience occurred to Gods command. Man was told that if he disobeyed, he would die and his flesh would be returned to the dust from which it came. Death was the penalty of disobedience, not life in eternal punishment, as most "fake religions" teach. The Bible speaks of resurrection, a returning back to life. Gods original plan for man did not include death, but everlasting life. "All those in the memorial tombs will hear his voice and come out" is the promise for our lost loved ones. A resurrection of the righteous and the unrighteous. The concept of a burning hell is a LIE!

In Christianity, nearly everyone who dies is awaiting the day of judgement. Only saints and direct agents of god are immediately in heaven. Christianity combined Jewish ideas and Hellenic ones about the afterlife, and they really don't sit together easily.

The Buddhist view has not been mentioned. There is some evidence Buddhists were present in the Middle East in the time of Jesus, and suggestions Buddhist teachings influenced the apparently monastic Essene Jews, the group who included Jesus.

The Buddhist view has a few strengths. Firstly, there are no eternities, every situation lasts only as long as it's causes and conditions. Secondly, the continuity between dieing and reborn things is not one of identity or essence but only of causes, like a candle lighting another candle. This is fundamentally more reconcilable in principle with thermodynamics and entropy.

For Buddhists, we are much more likely to be reborn in the hell-realm of ghosts and demons (parallel to animals and humans in our realm), than the heavenly realm of devas (jealous-gods, very like 'celebrities') and pure abodes (pure beings closer to divine principles, like biblical angels). This is not about a judgement, but a consequence of how we use our minds, of where we 'dwell' in our lives.

The Jewish rather than Hellenic tradition is all about the community, about the transmission of lived tradition, rather than pure abstract codified following of law (there is a case of the community going against god's decree, and later god agreeing that was the correct course). The concentration on revelation backed by prophecy, was much more of an experiential shamanic tradition, that evolved into a legalistic doctrinal system of having to master the texts and their interpretation to be allowed a voice in future community development/reform. Shabbat is meant to literally be practice for heaven, with not only reading religious texts but eating great food, with music and dance, with work even like flipping a light switch or pushing a pushchair outside the house forbidden, in order to simply be with your family, with your people. In the Jewish tradition only a special few are singled out for eternal punishment, most just cease, with a few who are ready attaining the state of being with god.

Dynamic conscious eternity makes no possible sense. But religious ideas, following Durkheim, can have social reality in the same way concepts like fiat currency do. Actual religious traditions have overwhelmingly focused on how we live our lives. But, we can see deep cross-cultural concerns with the idea of positive or negative residues to how we have lived, which seem to have emerged mainly from motivating warriors (hell is the Norse word for afterlife of the unworthy dead who did not die in battle). Religion is not epistemological, but a set of social technologies for rearranging the realtionship of the individual with the collective. The eagle that pecked out the liver of Prometheus wasn't a judgement from the gods, but his own guilt haunting him, the archetype of giving a gift to the unready. That, is the archetype that can make us ready to recieve; and to give.

In the Buddhist tradition, hells are to be avoided because there will be too much suffering to pursue much self-knowledge. But heavens are to be avoided too, because there will be too little suffering to prompt reflection. The best opportunity is this human life, full of mixed blessings. Dwell here, in these opportunities and lessons, right in this very moment.

You said: "In many religions, for example, the Abrahamic ones, there exists a place of eternal punishment for those who live in violation of God's commandments. Assuming an infinitely-long afterlife, in which "sinners" are punished with all the punishments deemed appropriate that Hell has to offer... doesn't that make God commit more evil than good by allowing those sinners to experience Hell? Surely, whatever evils committed while the person in question is alive are finite, while, as (to my understanding) the punishments suffered in Hell are infinite."

Both the early Jews (Israelites) and current Jews do not believe in the existence of Hell. It's not in their literature, the Pentatuch, even when the Levitical priesthood became infused with the Pharisees, Sadducees and Scribes who worked in synch to impose so many rules and regulations that the poor Jews couldn't even move on 'The Sabbath' without sinning.

But still --- there is no mention of hell.

Your: "God's Commandments" does not mention Hell at all. The Jews never did and don't now believe in Hell.

Hell arrives when the Roman Empire advocated a 'State Religion" creating the Holy Roman Catholic Church, where it wrote rules and inculcated heathen and pagan activities and beliefs into the 'faith' and totally cherry-picked parts of the Bible to suit their demonic needs.

This time period was told to the disciples when Jesus warned that there was going to be an introduction of apostasy and the congregations would suffer under false beliefs and fake leaders.

This new church needed to bring in some pagan beliefs so they could be attractive to those new members with their previous beliefs. It kept the pews full and the coffers jingling with money.

The RCC became a place of unspeakable horrors* and lies because they chose to keep with that policy, the belief of an everlasting Hell was a scary punishment as an inducement to control and ultimate liturgical power.
* The Crusades, for instance

But how can anyone NOT say that the following scripture destroys the concept of Hell: (in)...Describing what happens to a man at death, the Bible states: “He returneth to his earth; in that very day his thoughts perish.” (Psalm 146:4, KJ)

If the dead “no longer know anything” and their “thoughts perish,” how could they sense any torment in hell?

Another:" “The dead no longer know anything.”​—Ecclesiastes 9:5, NAB."

Many of the clergy because of Hellfire skepticism in their congregations and their empty seats, have backed off from teaching that hell is a place of literal fiery torment.

Rather, they promote a definition similar to that expressed in a Catechism of the Catholic Church, published in 1994. “The chief punishment of hell,” states that reference, “is eternal separation from God.” This too is another lie, even though they have softened the pagan concept a little bit.

Some still argue that there is indeed a Hell mentioned in the scriptures.

The original Greek word translated “hell” at Mark 9:47 is Geʹen·na. This word comes from the Hebrew Geh Hin·nomʹ, meaning “Valley of Hinnom.”

The Valley of Hinnom hugged the outskirts of ancient Jerusalem. In the days of the Israelite kings, it was used for child sacrifice​—a disgusting practice that God condemned.

God said that he would execute those who performed such an act of false worship. The Valley of Hinnom would then be called “the valley of slaughter,” where “the carcases of this people” would lie unburied. (Jeremiah 7:30-34, King James Version).

'Unburied' was an abomination to a Jew, and this painted a dire picture to them should they commit such a serious crime that they too might wind up unburied and shamed by being tossed over the wall onto a pile of other dead carcasses and garbage.

Assuming hypothetically for the sake of logical analysis that the doctrinal Hell you have described does exist: since that particular Hell is a natural feature of the Universe and not a real person or entity (it is rather a place or a spiritual condition) it cannot be evil -- because evil originates in the mind.

Psychology Today, Why Is There Evil? (2017, by Paul Thagard, PhD)

BBC Future, Psychology: the Man Who Studies Everyday Evil (2015, by David Robson)

Given that an all powerful god would have the ability to create a universe in which evil and hell are unnecessary, then he must by definition want there to be evil and hell. That sounds evil to me, especially within a Christian context.

A lot of comments and answers have touched on what's said to happen in hell, as if to excuse its existence - "it's not that bad!" - but I think it's irrelevant. The point is, in Christianity anyway, it is said that the worst offence is to deny Jesus, with the punishment being eternal separation from him. This means hell is the ultimate punishment. Whether you're tortured or not makes no difference.

Some answers have also claimed that god didn't actually create hell. My question would then be "what did?" Did something exist before god? A god that didn't create everything is not all powerful, so why call it god? This makes more sense in a Gnostic context.

I'm surprised by how so many explanations on here read like abusive relationships, as in, god created people so that they would love him, if they don't then they're put somewhere as punishment.

See Problem of Evil

A lot of answers have been dancing around the question, which is odd, because it's a very easy question to answer.

Any sentient being that created a place of endless suffering and in fact sent other sentient beings there to experience said endless suffering would be evil. Very, very, evil. Regardless of what those individuals did. It is a very thoroughly documented fact that severity of punishment has little to no effect on preventing an action, only certainty of being caught.

Any moral system that says otherwise is as useful as a logic system where True entails False. If it can ever not be evil to consign a sentient being to endless suffering, then the moral system has lost all useful meaning. A lot of religions don't say this though.

You specifically gave Abrahamic religions as an example of a group of religions that do say this, and while it's tempting to say that the founding documents for these religions often don't actually include Hell, the very fact that you think they say this is indicative of a very important point - there is a lot more to a religion than just the founding document.

There are a lot of modern pseudo-abrahamic religious groups (I'm genuinely not sure how else to describe them) which preach about an all powerful deity that created hell and actively sends sentient beings there. The deities described by these groups are very definitively evil. Even an all powerful being that created our universe (or any universe ultimately ruled by entropy(1)) would be evil, without need of making something even worse and then threatening it as punishment to sentient beings here.

1] The only justification for creating a universe with sentient beings in it and which is ruled by entropy is if you yourself are bound by entropy (and so not all powerful), cannot do better, and have a really -really- good reason for using up your own scarce resources in creating said universe at all. Why? Because entropy ensures, by it's very nature, scarcity and hardship.

Entropy

The simplest way to explain entropy is that it is disorder, or 'mixed up-ness' of a collection. If you don't like numbers, skip to the 'game part' below.

Consider a universe consisting of the the numbers 1 through 1000. They could be in increasing order from 1 to 1000 or they could be in a completely random order. The first would be a minimal entropy configuration and the second a maximum entropy configuration.

In a (simplified, so it fits in a single SE answer) entropically governed universe, to do something you must make use of amount of 'ordered-ness' to fuel that action. To 'fuel' an action, take two fixed blocks of numbers, add up each, and the difference between the higher block and the lower block is your 'fuel'. To use this fuel, you swap numbers so that the difference between the two blocks decreases. At first, in the perfectly ordered universe, there is plentiful fuel - you can take the block 1 through 10 (adding up to 55) and the block 991 to 1000 (adding up to 9955), and have 9900 fuel.

In the latter universe however, the fixed block of 10 numbers will be random values. Any given block will add up to roughly the same as another block of the same size (for there to be an expected difference, there would have to be a reason to, and there won't be enough fuel to do literally anything you actually want to do.

But is the former always guaranteed to become the latter? As it turns out, the answer to that question is exactly whether or not that universe entropically bound. The universe described above is entropically bound, eventually all blocks will add up to the same amount and no fuel to do anything will remain. To expend fuel, two blocks must move closer to each other in their sum. So at least one of the two blocks must move closer to a sum of 5000 and the other block can only move away from 5000 if it itself is between the block that moves closer to 5000 and 5000. This may not be easy to picture in your head, but that's okay, you don't have to!

The Game Part

Take a piece of paper, and put some coins on it, so that no two coins line up horizontally (because you'll be sliding them back and forth, horizontally). The fuel action above is the same as sliding two coins horizontally until they line up vertically, equally between where they were before. If you play this for a while, your coins will inevitably end up as a straight line and your coiniverse will have experienced horizontal sliding death. This is entropy.

All useful actions, all useful resources, all things you actually want to do in an entropically governed universe require sliding a coin some minimum amount.

By all evidence, we appear to live as something like a collections of these coins a very big such piece of paper, with more complicated rules that ultimately follow the same limitations.

A) But what about fixing it? Re-ordering it to have more fuel?

If you can do this, some reset option or if the action to re-order the numbers is cheaper than the new fuel it makes, then the universe is not entropically governed and you can do useful actions that you want to do forever. All evidence suggests this is not the universe we live in.

B) What about getting fuel from somewhere else?

If that somewhere else is the same universe, then you are only delaying the problem, increasing your starting fuel capacity does not prevent you from running out. If that somewhere else is not the same universe and can be accessed indefinitely for more fuel than the cost, then as in A, you are not in an entropically governed universe. All evidence suggests this is not the universe we live in.

C) What about a virtual reality where nothing is limited?

Simulating any change in that virtual reality is a useful action, and not something you can do forever. This is simply making life more efficient, so it can last longer and have more experiences before running out of fuel. It is pretending the universe is a better place than it actually is.

D) What if the universe is infinite?

Then it depends on how far away you can reach, and what the largest sum of a block is. If you have a location, and you have to expend fuel available locally to reach further away, then you may or may not live in an entropically bound universe depending on how expensive it is to reach some distance away, even if block sums can increase without bound. We are not sure if our universe is infinite, but it does appear to have an upper bound on the difference in fuel fuel in an area (the Bekenstein bound) as well as definitely being expensive to reach for fuel further away.

E) This sounds like an oversimplification of a complex concept

That's because it is. There is a lot (a lot a lot) of math this skips over, but the core intuition should be close enough to convey the concept. The fuel concept has a much deeper statement and implication in the math, for example.

I'll join the rest and reject outright the proposition that any sin is finite.

Because literally nothing God does can be counted as wrong (without invoking a contradiction), God has not wronged you, and therefore any wrong you do to Him is infinitely disproportionate, and that merits an infinitely disproportionate response.

If you say that the sin was against your fellow man, and not God, you are mistaken; in order to commit that sin against some other fellow, you first made your heart the throne of hate, greed, lust, pride, or some other sentiment that is contrary to God; and that heart is God's property.

Thus, hell is an eternity of mind-bendingly intense suffering; not because God delights in making its inmates suffer, but because that is the only way for justice to be done.