I know lots of single parents. But frankly, it's even harder to get together with my single mom friends than with my child-free friends or married mom friends because our custody schedules never coincide. Or their kids' naptime conflicts with our free time and my gym daycare availability conflicts with their free time.
I'm social, but pretty tapped out. When my ex has my daughter, I go out with my kid-free friends. But the rest of the time we're balancing a buttload of activities - sports, dance, girl scouts, pta stuff, cultural stuff, other volunteer stuff, my workouts, house cleaning, yard work, errands. I find myself saying "yes, we should do a playdate" but it never gets scheduled because we're all so busy.
hang in there. If your kid is really young, it's just a matter of time before there'll be more divorces. Also, some of them are quiet about it - most people from my daughter's school don't actually know I'm single until I specifically tell them because my daughter's dad shows up to stuff with me and we get along.