If Cruz was challenged in court, it might go the the Supreme Court. More likely, it wouldn’t get that far. However, it would be reasonable to ask a court if someone with a US mother, born overseas, could run.
It might be reasonable to ask, but my bet is that a court will tell you that it does not issue advisory opinions and that it has no role to play in the selection of a president.
Similarly, if the House of Representatives were to impeach Obama and cite as a high crime and misdemeanor his "continuing fraud about his qualifications to be president," and if the Senate then voted for conviction and removal, the Supreme Court would not assist Obama by weighing the evidence for and against him. The Supreme Court has no role in the impeachment process (other than that the Chief Justice preside over the Senate during the trial).
The Supreme Court does not get to decide everything in this country.