You don't bring out your proof AFTER an appeal. You don't get to appeal on the basis of the fact that you didn't consider the lower courts to be serious enough to make a proper effort - that's not what an appeal is for. If Trump has proof he has to show it NOW - as in, he's already late to do that.
SCOTUS are not impressed by "the REAL proof is something I can only show YOU". That is not a thing in law and never was.