Growing up, about 10 families all had kids within 18 months of each other, within a 3 mile radius. The parents all got together and worked out a time share agreement where all 10 kids would get dropped off from roughly 9-5 at one parent's house, then a different parent's house the next day, etc so that one house had 10 kids for an entire day, every two weeks. This happened from about age 0-3 pretty religiously. It worked out partly because all the parents were in the same age/ethnic/religious/income group, but it might work across wider groups. It didn't cost anything. We called it the "babysitting group" and 30+ years later I'm still pretty good friends with most of the kids in our group.

I think "modern" parents take their kids to the park to try and socialize with other parents/kids but the unstructured method doesn't seem as effective.