Now, a better question is if the new President had ever really been the VP for more than a nanosecond.
That would have to be the case for that individual to have succeeded to the Presidency, unless otherwise placed at the top of the line of succession. The VP-elect takes the oath of office before the President-elect, just before noon. At noon, the Presidency would be officially vacant and the new VP would presumably take the oath of office as President of the United States. It would be redundant, but I think it would be necessary to take the oath of office almost back-to-back for Vice President and then President.
They'd become President at exactly noon, and would never be VP.That's not possible. Unless that individual is at the top of the line of succession (as Vice President), there's no other way to become President. The only alternative would be if the President-elect had died prior to the meeting of the Electoral College and the electors had chosen the VP-elect to be the new President-elect.
The Vice President-
elect does not have a place in the line of succession. He/she would have to first take the oath of office for Vice President. If that didn't happen, the Speaker of the House would assume the Presidency as the highest individual in the line of succession.