I’ve seen early episodes of Family Guy when Peter and Joe first met. Peter didn’t like him much at first. I’m not sure if I missed the episodes where they became friends and Joe started hanging out with the guys or what happened. How did Joe go from Peter’s annoying neighbor to one of his best friends?
Peter meets Joe when Joe moves in next door.
From the episode, A Hero Sits Next Door:
Meanwhile, Lois goes with her youngest son, Stewie, to meet the new neighbors. She is greeted by Bonnie Swanson and soon after meets her husband, Joe, while Meg falls in love with Joe and Bonnie's son, Kevin. When Peter comes home he is rude to the Swansons.
After some softball, Joe being a popular hero, and a failed heist, they pretty much become friends after that.
I don’t think that there is actually an explanation about how they met. In fact, I don’t think there’s ever been any explanation about how Peter met Cleveland or Quagmire either.
I might be wrong though. I’ve watched tons of family guy in the past but I haven’t seen all the episodes so I might have missed one about them meeting.