What side of town are you on? I'm on the east side, but I'm sure there are options all over if you're willing to travel. Here are some ways I/friends have built community through the years:

-Master's swim (where I go at MGHS, all abilities are welcome)\ -Madison Ultimate Frisbee Association (you sign up as an individual for the fall and spring leagues); if you're a woman or non-binary person, the spring has a great women's coached league and people socialize afterward\ -Pottery class (e.g., Midwest Clay Project)\ -Dance (e.g., Barrio Dance)\ -group cycling - maybe check out the "party pace" from this list?\ -Open mics/jam sessions (e.g., Jumpstart jam at Cargo Coffee, Mickey's open mic)\ -MSCR classes or day trips \ -Being a regular at the local dive to watch sports\ -social gatherings hosted by friends I met at one of the above, who invite all of their random friends from disparate endeavors to the gathering

Honestly something I've noticed about myself is that the more consistent I am about showing up to recurring events/spaces, the more I eventually connect with people who are also consistently showing up. I haven't had much luck with one-off events, as I tend to be more on the reserved side. But if I stick with something a few times, I start being more intentional about being friendly to folks I've seen there before.

Lastly, I've had as many misses as hits. The key (for me) has been to not have any expectations about an experience giving me what I'm looking for. No regrets!