The Constitution spells out a few qualifications for President:
- You have to be at least 35.
- You have to be a natural-born citizen.
- You must have lived in the US for at least 14 years.
- You can't have engaged in insurrection or rebellion after swearing to support the Constitution as an officer of the United States.
Why do you think exactly one of these should be irrelevant until decided by a criminal court?
The authors of the 14th Amendment could have phrased it so that a
conviction for insurrection was required; they didn't. Why do you think that is? Personally, I think this had to have been a deliberate choice.