it's the only way it works. It took me MONTHS to get a hold of the number of my son's best friend's parents so that now we can organize maybe an afternoon of play every 4-5 weeks.
I thought a prime time for contacting the parents is right after school when picking up the kid. Everyone is there waiting, so it's just natural to chit chat, esp when the kids are friends.
I'd count also those memorable school talent shows/performances and events. Another reach out avenue is volunteering, these have a higher chance to match parents with similar availability at least.