Did Santa Claus exist? There may been a Nikolaos of Myra in present day Turkey who was an early bishop. There are a bunch of legends around him, including that he punched a guy at the First Council of Nicea. But anything record about him at the time would likely have been public relations, and then afterwards stories made up around him, so who knows.

He got made a saint, and so lots more fan fiction was made up about him. At some point he got syncretized with various non-Christian mythology as the Christmas St. Nick, rebooted in the poem "The Night Before Christmas", again in "The Life and Adventures of Santa Claus" by Frank Baum (who also wrote The Wizard of Oz). But it was really when it was adopted for advertising in the commercialization of Christmas and by Hollywood that the story took off.

Now for a little kid who believes in Santa Claus, none of that is as all relevant. For them Santa Claus is an imaginary friend.

Is there any meaningful sense to say that there was a historical Santa Claus in some guy in Turkey who may have punched another guy in 325 AD over a bit of theological minutia involving the nature of the trinity?