Wish I knew how to make friends

I'm on my early 20s and I have a life ahead of me, but ever since I left uni I can't help but notice people are not as friendly. I don't have many friends or people to fall back on that I really trust or even hang out with.

Funnily enough, at work there's this new girl who caught my eye ever since her first day and because of past trauma I have not wanted to engage with her (she's far from me either way so it's not that hard), but today I decided to approach because honestly I'll survive the worse case scenario, but I froze, like every time I get the chance to do a little comment I freeze. I will get near her with some excuse in my head and I just follow through the excuse instead of talking to her.

I don't want to interrupt her space and I don't want people to comment either, but even if I didn't care about any of that, for some reason I cannot bring myself to do anything and I hate it, she's not the only one it happens, to be honest I haven't had that feeling of wanting to befriend someone in a long time so it sucks.