Ayer, MA (maybe not central MA enough for you?) has a "Little Kickers" team--it's all under-fours. My DD started at about 2 1/2; DS started at 18 months. It's really silly and ridiculous, but gets the kids out onto the field, each with his or her own ball, doing games like "red light, green light" and "Simon Says," with some other soccer drills sneaked in. No real games or anything, and all of the kids are together, not divided into teams. They get a team tee-shirt and a trophy at the end of the season. Seasons are in the spring and fall; the spring season started last week.
I can't imagine this sort of thing is unique to Ayer; much luck in finding something close to you!