I don't know how to look for a prototype -- it would be pretty ancient. I suspect that the AABA form (and there's more to it than just the letters!) had been floating around for a long while. Here's "Beautiful Dreamer" by Stephen Foster -- 1864. The bridge (B section) even ends on the 5 chord, which is standard bridge behaviour. It wasn't a new invention but it emerged from the woodwork to become the dominant form in pop music until… maybe Rock & Roll.

Beautiful Dreamer