Before starting university, one of my friends gave me the advice "In the first week, talk to as many people as physically possible". My entire group of friends at this point were extremely socially awkward and so was this guy, but he was insistent that I should make sure I do that.
So, I went to university, and for the first week powered through the anxiety in order to go to every social event and speak to as many people as I could (and I mean literally walking up to, introducing myself to, and making small talk with literally every single person I could in the amount of time available) and it worked! While the people I met in that week were never exactly close friends, and in fact some of them turned out to be complete assholes, that one week led to me being invited out to other social events and meeting people who I actually became friends with and have remained so ever since.
I won't lie, it was damn difficult and it took a lot of carefully controlled alcohol intake (enough to not hide in a corner hyperventilating but not so much that I couldn't stand up straight) in order to manage it, but it was definitely worth it.