That’s a bit of an unknown. It’s an American thing, that much we do know. What other culture holds five-inch-thick cake layers in such high esteem? As for exactly when and where angel food cake first appeared in America, that’s tougher to determine. People like to say Pennsylvania Dutch country, but that’s really just a guess, albeit a safe one since so much in the American home baking canon has come from that region.
As for when, another safe guess is the late 1880’s, since those are the days of the so-called home baking explosion, when post-Civil War industry turned its attention to supplying American households with consumer goods, notably stoves, baking forms and utensils. The first mentions of “angel cake” or “angel food cake” appeared in print about that time.