This might get bumped to Elections, but I am intending this as a more straightforward query rather than a debate.
The office of President in the US has three constitutional requirements, 1) natural born citizen, 2) over age 35, and 3) a resident of the United States at least 14 years.
You could ostensibly prove your age and citizenship with a birth certificate. Conspiracy theories aside, it is the best and official proof you have of the circumstances of your birth.
What I want to focus on is what would constitute proof of residency for 14 years? In this modern age US citizens living abroad are required to file income tax returns and many I know use a family address in the States. What else might suffice?