Really? I tried and tried to parse it that way before I said anything, and I'm still trying, and I can't. "Infancy of painting" means "when painting was first being developed" to me, not "when infants paint." I don't think it's changed since then, and even if it has, surely if you meant an ongoing habit of small children you would say "write," not "wrote"?

Maybe he's extrapolating from the practices of small children back to the invention of painting?