Qualifications are verified when the EV are received by Congress in joint session as per the Constitution. At any point up till then there is no constitutional prohibition against as unqualified candidate running or even winning.
“Qualifications are verified when the EV are received by Congress in joint session as per the Constitution.”
The qualifications of ELECTORS are certified and members of the House and the Senate can raise objections to them.
You are saying that that the Clerk of the Senate verifies age, citizenship, etc. after the electoral votes are counted.
I have searched United States Code Title III, Chapter I: Presidential Elections And Vacancies - there is NO provision for the Senate Clerk (OR ANYONE, FOR THAT MATTER to do ANY such thing.