The baby on the doorstep is a staple of old fashioned fiction (and cartoons) to the point of parody. It’s always in a basket and usually with a note - the ultimate ring the bell and run prank.
Now, I know churches and monasteries are classic places to leave your baby from antiquity to the modern Safe Harbor law. But what about the cliched private home? Did that happen, and did the occupants keep the baby like they do in the cartoons?