Membership organizations - country clubs, professional associations, alumni networks, charitable boards
Personal introductions and referrals - being introduced through mutual acquaintances
Cultural and civic participation - involvement in local institutions, community organizations, religious groups
But most of these don't exist or help with socializing and making new connections where I live (medium sized European university city).
Everyone here only hangs out with their family and school/university mates and that's it. Any other available events are either for college students or lonely retirees but nothing in between.
If you can get a few people from 2 of these groups together more than once, you've started solving this problem. Of course keeping it going for a long time is a challenge, and you want to avoid always being in the situation where you are doing all the work and others aren't contributing, but it gets easier and better with experience.