The 12th Amendment says that whoever receives a majority of the votes of the Electors “shall be the President.”
Obviously determining eligibility must be accomplished before or at the early January Joint Session of Congress that is held to count and certify the votes of the Electors.
“No Person except a natural born Citizen... shall be eligible to the Office of President”. If a person is not a natural born citizen then they can not be President, it is an impossibility. Election does not launder ineligibility. To claim so would make Article 2 moot.