I was in the same boat when I moved to Liverpool for LJMU 3 years ago. I did drink quite a bit, unlike yourself. But I managed to make a few friends who were only really drinking buddies at the start. I didn't join a society straight away but managed to make friends in lectures simply by asking if I could sit with people/walk to uni with them. Half way through first year I joined my first society and met so many friends. You have to remember, a lot of societies will also hold sober socials such as movie nights or study sessions, so it is still worth joining societies even if you aren't a huge drinker. I also got a job in my first week of uni, which again helped alot with making friends.
I would say try not to stress too much, and I'm sure you will make friends 😊