We lived in a country with a tropical climate where babies rarely wore nappies. They were carried all the time by their mothers, who quickly became attuned to their baby and could sense when the baby was about to perform. At that point they would just hold the baby over a suitable place and that was it. They would have a cloth underneath the baby sometimes but they had nothing fitted and as they grew older, ran about with bare bottoms. These children were trained pretty quickly, as you can imagine!
It happened that way because nappies were unaffordable (putting your child in nappies was a way of boasting about your financial status) and most people had nowhere to wash them anyway, except ditches or rivers. People didn’t have prams or even cots, which they called boxes. You rarely heard a baby crying as with large family there was always someone to take care of them.
It would be hard to live like that in a cold westernised country, though.