Yes. The constitution is actually shockingly specific about what the qualifications are. Article II, Section 1, Clause 5:
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
No other qualifications can be considered, barring a Constitutional Amendment.
Where does it say that no other qualifications can be considered? It certainly lists a lot of qualifications that are required, but doesn't say that it's an exhaustive list.
Those are not the minimum qualifications. They should be read as “anyone who meets them is eligible” rather than “no one who fails to meet them is eligible.” The Rehnquist court found that states could not add a felony exclusion for Congressional candidates in the 1990s and that is broadly considered to extend to the Presidency as well. https://www.oyez.org/cases/1994/93-1456
If the constitution doesn’t say it, it’s not typically intended to be assumed true. The constitution doesn’t say that felons can’t be president - so we can’t assume that the states or congress could pass laws forbidding them from being president. It specifically says you can’t be president if you’re 34 or were not born a US citizen. If the writers wanted to exclude felons, they would have said so.
The 35 year old requirement seems bizarrely high to me, I can't see why a smart and capable 32 year old should be prevented from running for the office. A minimum age makes sense, but it's weird that it's far removed from when most states start to legally treat kids as adults (anywhere from 16 to 21).