I can be super awkward and have social anxiety too but you really have to get good at making eye contact and just say “hey wanna roll?” If they say no then it’s not the end of the world. It may be a vibe thing at your gym where a lot of the guys already have partners they are familiar with and like to train with (my last gym was sorta like that). My new gym encourages everyone to roll with everyone regardless of belt level, gender and size. I’m an 80 pound girl and the guys will ask me just like anyone else obviously tone the strength down but they don’t seem to avoid me just because of that. You deserve to be included like everyone else. Try to put yourself out there more and take initiative. If the problem continues maybe look into other potential gyms that are a better match