Over the past few months (before quarantines started) I've gotten started in the dating game for the first time. If in my general social environment (physical sciences), I take an interest in someone, I generally try to be honest about it (not necessarily saying so explicitly, but letting it shine through in my words and demeanor). At least in my general stomping grounds, I think I'm reasonably good-looking, and women seem to find me funny and engaging.

I worry about the little things. I notice some girls who appear to be interested, act nicer to me one-on-one than around other people, and react strongly to an occasional, unfortunate choice of words on my part. Because of factors like these I worry about being mistrusted, and due to social ineptitude made some unfortunate moves (waiting too late to ask and appearing desperate or indecisive, not taking things forward even when a girl initiates, etc.). Out of an abundance of caution, I frequently just give up on all social interaction with a girl if I make even the slightest social faux pas (real or imagined). What are some good ways to establish trust, without coming off as under confident or insincere?

EDIT: Edited for clarity. I'm perfectly capable of taking "no" for an answer, I'm not some sort of excessively persistent, frat boy "trp alpha". I want an equal relationship founded on mutual respect, not to coerce and manipulate anyone into something they don't want. This is a question of social ettiquette: years of being bullied/harassed (you can check my post history for details) have made it difficult to read or convey subtlety and I fear coming off more strongly than I intend.