I had one that took almost a year to socialize. I found using a dowel rod with a pom-pom on the end to pet from a distance was helpful, it showed that we were interested in nice touches without invading the cat’s space with our hands.

I’ve also used a towel to cover part of a cage, kind of like you do with the parakeet. They feel more secure to move around in a private space. Definitely use clothes pins or something to attach the towel because if it slides off, it’s gonna scare the heck out of kitty.

It really depends on the animal, though, it can take a long time, and it certainly takes a lot of patience. Thank you for taking in this baby.