There were cloth diapers that you wash and reuse as depicted by Adrien Brouwer's painting The Unpleasant Task of a Father. Other cultures might use other materials, for example the ancient Inuit would use reindeer moss stuffed into seal skin "rubber pants"

Diapers (nappies) were all cloth until very recently, and it's still very common in Europe for environmental reasons. There are nappy-washing services in most large urban areas.

BTW, there is a third alternative. In China it's still common to see toddlers wearing leggings but no covering over the crotch so that they can relieve themselves in public. Does anyone know if this was done in Europe?