After asking if Revivify is commonly used, I started searching for ways that I could cast Find Familiar, since that was the only other spell that I had trouble justifying an entire feat for. Answers can include magic items that provide a 1st level Wizard spell, like the Witherbloom, Quandrix, and Lorehold Primers, or allow another PC to provide me the spell itself, like the Ring of Spell Storing. Feats are allowed also, but please exclude class and racial abilities if possible, as my character is already pretty much locked in on the path he'll take. Lastly, use official material only, with no third-party or UA sources.
If you can get yourself a Spellwrought Tattoo of Find Familiar spell, anyone can use it, and it doesn't require attunement. Using the Spellwrought Tattoo doesn't require spellcasting ability, unlike Spell Scroll, which requires the spell to be in your class spell list.
It is one-time use only, but probably okay for Find Familiar, since the result is permanent (until the familiar is killed).
(Some backstory: my monk character in a PBP campaign is also looking to get a familiar. We have easy access to magic items, and without taking a feat or multiclassing, Spellwrought Tattoo is the only considerable option I have. It requires no attunement, and is not too expensive in the server I play in. Ring of Spell Storing takes an attunement, although for Find Familiar arguably you can just borrow it to cast it once then returns it, but it's not allowed in the server I play in.)
It's technically by way of a feat, but if your campaign allows the Strixhaven backgrounds (some don't, as they're overpowered relative to most backgrounds), choosing Lorehold Student, Quandrix Student, or Witherbloom Student all give you the school's associated version of the Strixhaven Initiate feat for free as part of the background, which grants you two cantrips (from a list of three) and a 1st level spell from one of two spell lists. Those three schools have the Wizard list as one of their options, and can therefore provide you with Find Familiar. You can cast it once a day for free, and it's a known spell that can be cast with any other spell slots you have, should you need to do so.
Aside from that, there are two other feats that will grant access if you choose the Wizard spell list variant of the feat:
- Magic Initiate
- Ritual Caster
A Ring of Spell Storing is another option, being a moderately cumbersome but reusable way of achieving this with no direct resource cost if someone else in the party can cast the spell (just the time cost of attuning it to someone else to store the spell in it for you, then reattuning it back to yourself). (Per @Senmurv) The Spell Bottle (from Explorer's Guide to Wildemount) is a more convenient equivalent (no attunement shuffle required), but it's also a Legendary rarity item, where the ring is merely Rare, so (according to the usual magic item rarity by level guidelines) the bottle wouldn't be available until level 17.
Buy it as a service from a lvl 10 Chronurgy Wizard using Arcane Abeyance
The feature allows the wizard to cast a spell into a bead, and whoever releases the spell from the bead is treated as the caster of the spell. This gives you a single cast of the spell, but can be purchased again if needed.