Putting yourself out there and edging over the "acquittance" level

Hello guys--

it sounds super lame of me, but I will just state my case: how do you go past the awkward acquittance stage and become friends with cool people around you? There's so many people that I meet at my classes or during my club stuff at college that seem super chill and I would like to be friends, but I always find myself overthinking and not able to make it past the casual-hello-at-the-library-before-we-go-back-to-familiar-friend-group stage, if that makes sense.