How do I get closer to someone?

The past month has been super hard for me. I'm a freshman in college (19F) and broke up with my girlfriend not too long ago. Since then I have had no one. My only friend had to drop out and I hardly see her since that happened and we're constantly fighting over stupid little things

Earlier this week I was waiting in line to sign my attendance sheet for a lecture and the person in front of me turned around and started talking to me

It was simple. Just complementing my hair but today in class she waved and said hi so it wasn't just a one time thing

I checked to see where she sat and it seems like she has 2 people she sits next to and talks to so if i get close to her it could be a good opportunity to get closer to multiple people which I desperately desperately need

My only problem is how tf do I get closer to her. I don't know her name so I can't find her socials and message her and I also have to make sure that the two people she talks and sits next to would be okay with me sitting with them

Im not quite sure if they sit in the same place every lecture but I am gonna keep track of it and see if I can get to class first and sit there so instead it'd be them sitting next to me instead of me sitting next to them

Diesn anyone have some advice. I need it