Most of my deep friendships were through friends and family. A handful at work/school. And it is the same way for most people I know. But I'm not American, so that's that.
Making friends through work and school are pretty much exactly what I described. You go to a place with people, you meet a lot of people, and some of the shallow acquaintances end up becoming long term friends.
It can be any other activity that requires more than one person. For example I started going to dance classes with my partner in november and what was just awkward "hello there" interactions before the holidays when we had to swap dance partners is now a bit more comfortable and we exchange a bit much and even have a chit chat after class at the door. It is waaaaaay too early to know if it will create new long term friends but the dynamic is here and after just a few weeks I can already spot the people I have absolutely no wish to know more about and those that I feel natural chatting with.