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The Magic Initiate feat allows a character to take two Cantrips and one 1st level spell from a casting class of their choice.

Find Familiar is a 1st level spell that is a Ritual spell with casting time of 1 hour.

If a caster does not possess the Ritual Casting skill (such as Sorcerer), are they able to cast Find Familiar if they take Wizard spells as part of the Magic Initiate feat?

In 5th Edition D&D, a Ritual spell means the spell may be cast as a ritual, not that it must be cast as a Ritual.

From the Player's Handbook, regarding Ritual Spellcasting:

Rituals

Certain spells have a special tag: ritual. Such a spell can be cast following the normal rules for spellcasting, or the spell can be cast as a ritual. The ritual version of a spell takes 10 minutes longer to cast than normal.

It also doesn't expend a spell slot, which means the ritual version of a spell can't be cast at a higher level.

To cast a spell as a ritual, a spellcaster must have a feature that grants the ability to do so. The cleric and the druid, for example, have such a feature. The caster must also have the spell prepared or on his or her list of spells known, unless the character's ritual feature specifies otherwise, as the wizard's does.

So if you get the Find Familiar spell through Magic Initiate, but don't have the ability to perform Ritual Casting, you are still able to perform the spell as normal. You simply won't be able to cast it using the Ritual Spellcasting rules.

Yes and No.

Yes, they can take and cast find familar

The feat Magic Initiate reads:

Choose a class: bard, cleric, druid, sorcerer, warlock, or wizard. You learn two cantrips of your choice from that class's spell list.

In addition, choose one 1st-level spell from that same list. You learn that spell and, using this feat, can cast it at its lowest level. Once you cast it in this way, you must finish a long rest before you can cast it in this way again.

Find familiar is a First Level spell. If you choose the wizard spell list, then you can choose that spell, and be cast as described in the Feat. It takes only the casting time, and not the extra ritual time to do so.

Can't cast it as a Ritual

Unless they have ritual casting from their class or another source, they may not ritual cast the spell. You would have to be your single spell per day used through the feat, or a spell slot if find familiar is on your class list.