Definitely possible. The nosiest thing would be banging on chisels, I've seen a hollow chisel mortiser recommended as a power tool well suited to apartments if you're not going all in on hand tools: https://www.finewoodworking.com/project-guides/shop-machines...

And here's an example of an apartment woodshop, you can get started with many less tools than this: https://www.youtube.com/watch?v=ybvuuVRlSWc

r/handtools is another good place for questions/information on that.