As a matter of process, the federal government can't operate that way.
It must assume the president is the President, and the congress is the Congress, and the laws enacted by the same are valid.
If, in the future, it's found that some aspect of the ruling order was legally invalid, e.g., the president wasn't eligible, then the outcome must depend upon the opinions of the sitting congress.
Of course, there are hard cases. E.g., a Supreme Court justice confirmed by one vote. But one of his votes turns out have stolen his senatorial election. What is to be done?
Answer: He's Mr Justice Whomever. Unless a majority of the House and two thirds of the Senate ...
And that's how the cookie crumbles.
Sorry but I doubt that fraud requires two-thirds of any vote it just requires criminal investigation.