The great folklore theoretician Carl Wilhelm von Sydow (1878-1952) classified entities like Santa Claus as "ficts" - stories told to children to be believed, while not believed by the adults. (von Sydow was my mentor's mentor; see my brief essay, Nazis, Trolls and the Grateful Dead.)

In modern American culture, ficts include the tooth fairy, the Easter Bunny, the stork, the boogeyman, and, of course, Santa Claus. Ficts are ubiquitous in other cultures. I suspect we can find examples in ancient cultures, but we need to have someone who knows ancient cultures to weigh in. You are probably not getting answers to this question because one must understand the "cultural place" of Santa Claus to recognize equivalents in other cultures and historic times.

The stork gives us an opportunity to understand the history of ficts and how they can originate, in this case, likely reaching back to late medieval times. An excerpt from my Introduction to Folklore:

One common practice related to childbirth resulted in a traditional fict of western culture. A woman was in jeopardy during birth because a host of supernatural creatures might attempt to abduct her and leave a replica in her place that would appear to be her corpse. To avoid such a fate, people ushered children outside and sealed the house. When the birth was complete, the doors and windows could be reopened and the children returned. There was a need, however, to explain the arrival of the infant.

Parents wanting to avoid the topic of conception and childbirth relied on the fact that the only opening to the house was the chimney. Coincidentally, European peasants had observed that storks nested on the little-used gallows or “Catherine” wheel in towns. These looked like wagon wheels positioned horizontally on tall poles, and storks found them a safe place to nest. The birds were regarded as good luck, so it was not uncommon for people to construct a similar wheel on top of their roofs to attract storks. When children asked about the origin of the infant, it was easy to suggest that it had arrived by way of the chimney and that the stork had accomplished this deed.