I'm not sure what you're angle is here, but I should point out the above has already been done. With hard math. Turns out Santa's yearly trip around the world, to the household of every morally sound child on Earth, violates Einstein's laws of relativity.
(the thing that makes this really funny is,
it's not a joke!)
I know, I have also done those same calculations when I studied physics years ago.
However, you could easily claim that he had powers that went beyond those limits (or that there really aren't all that many good children).
Just like you would have a hard time disproving god. Or magic. Or the soul.
Just about anything that, by definition, is outside our reference frame, is, let's just say difficult, to prove.
You could claim that it makes no sense that some alien, with the help of psychiatrists, brought billions of his people to Earth in a DC-8-like spacecraft, stacked them around volcanoes and killed them using hydrogen bombs, for their souls to infect humans.
But if he had "special powers", it takes the whole mess outside of our frame of reference.
Or that Adam and Eve's sons somehow found daughters, and yet we are not inbred.
Any fantastic claim has to show that it is itself reliable, otherwise it is not in the real of science.
The whole "show me the math that proves X does exists" is bollocks.*
*Where X can be anything fantastic, like God, or Xenu, or Homeopathy, wait, that last one actually claims to function inside normal laws of nature, and has been proven to be placebo. Yes, I have a special, hateful, place in my heart for homeopathy, and the Xenu story is just so fun.