If Cruz is the nominee, that "finding" will only be whatever traction it gets in the press. It will affect some voters, and there is only downside risk to Cruz on that (meaning the most votes come if he is clearly qualified, and gets fewer votes if there is a cloud).
If Cruz becomes president-elect, Congress can find him unqualified. I doubt it would, but it could, meaning it has the constitutional authority. Either way Congress goes, a lawsuit could be taken to SCOTUS between the time Congress finds Cruz qualified, and swearing in. SCOTUS could refuse to adjudicate the question (meaning there is no check on Congress seating an unqualified president-elect), or take it up.
There is no new nominee. The unqualified person finds something else to do, and the law seats the veep-elect. If the veep-elect isn't qualified either see 3 USC for next in line.
Works for Me!
Ted Cruz for President (97%) / Mike Lee for Vice President (100%)
https://www.conservativereview.com/scorecard