I'm not sure Team Trump wants to get anywhere near the Supreme Court, where defeat would be final and, because Trump appointed three Justices, unassailable. The Supreme Court has original jurisdiction over certain cases in which a state is a party. If the Trumpsters really wanted to get there, they could almost certainly fashion their complaint as qualifying.
For example, SCOTUS has original jurisdiction over suits between states. If a "Biden" state has allegedly violated the US Constitution by not sending electors in the manner prescribed by its legislature (because of fraud, say), a "Trump" state might claim that its right to have the President elected in a certain way has been violated. If Trump had a real case with real evidence, at least some effort might be made in that direction. (Of course, if Trump had a real case with real evidence, he could win in lower courts.)
Trump just wants to be seen as "going down fighting." He is using the lower courts to burnish his brand among his less astute worshippers, which, sadly, are legion. As a wise man once said, no one ever went broke underestimating the intelligence of the American public.