Back when I lived in Madrid, and I was 30, I hit a pick-up game twice. But it started at 10:30 p.m. and was an hour by metro there and 1.5 hours coming home. And that to play on hard pack dirt with 30 other people I didn’t know. Since I had to be up at 5:30, I couldn't do that.
About 10 years ago I played some in an early-morning outdoor pickup group (indoors in winter at a church gym) and played at the crack of dawn (6, I think). The ages were mixed but trended toward 18-35, and they played pretty hard -- a heck of a workout a middle-aged guy like me. It felt great once I got going, but the first 10 minutes were usually brutal and I honestly preferred the late-night stuff. To the OP's original post, maybe here's an answer: We played on a field at a local university that I don't think we were supposed to be on, but at that hour no one seemed to care. Get the kids out at dawn and sneak 'em onto someone's field? ;-)
Well, it seems he wants the ORGANIZED games to be longer. You're not going to be able to "sneak on" a field for an organized game. To me, if you want more playing time for the kid, organize/schedule some "pick up" games at your local park. Done.