I think most people find it simultaneously wonderful and extremely boring to be at home with kids for extended periods, so quite a few seize any chance of having a conversation with another adult. The playgrounds are full of bored parents, and everyone has one or more tiny, human conversation starters.
Kindergarten is pretty good as well for meeting people. When a three year old is invited to birthday party, they kind of have to have a parent along for the event.
Somewhat specific to my locality (Sweden), there is 15 hours per week of free kindergarten for kids with stay-at-home parents. In my city there are specific drop-off and pickup times for those children, which means that six times per week you meet relaxed and slightly bored other parents, who have kids in the same group as you. This essentially always means that you hang around the yard for a bit and socialize.
Three new friends in two years, six if one counts spouses. That is the same amount that I made in the preceeding ten years!