Under the Electoral College system, Cruz would have no standing to bring the matter before the Supreme Court until he was actually elected President. Cruz is not really running for President and neither is anyone else. Cruz is running to have the opportunity to select a set of Electors to go to the Electoral College and cast votes in his name.
The issue of eligibility is first raised at the Electoral College. If the electors determine that a candidate does not meet the eligibility requirements, then they should not vote for that person or abstain from voting on principle (we see a lot of those "principled" people here). If after the votes are cast, Cruz is elected, then the matter is referred to Congress who has the opportunity to once again check to see if Ted Cruz meets the eligibility requirements. If Congress votes to certify the election then Ted Cruz becomes president. The Supreme Court has no jurisdiction after that to undo the election. Marbury v. Madison did not give the power to the Supreme Court to undo a presidential election after it is certified by congress, nor does the Supreme Court have the authority to rule on the eligibility of a candidate to take office. The Constitution is clear that in regard to the eligibility of anyone to serve in Congress or the Presidency, the power to make that determination is solely in the Legislative body.
Ted Cruz would be an idiot to even try to bring a suit for declaratory judgment as to his eligibility.
The Congress is not going to undo the election and neither is the Electoral College. This is a complete and total non-issue. But then there are the purists that would rather see America go into the toilet than to have someone elected with solid conservative credentials and a questionable pedigree.
Just remind yourself how many cases have been brought forth, and won, by libs going to court.
It's inconceivable you don't think this is one of the ways libs win. They win through lawfare as much or more than any of their other tactics.