[reg45]

Alexander Hamilton would have been eligible to be President, because he was a resident of the United States AT THE TIME OF THE IMPLEMENTATION OF THE CONSTITUTION OF 1787. All residents of the United States at that time were considered natural born. Otherwise, no one born prior to the adoption of the 1787 Constitution, could be a natural born citizen of the United States, because, prior to the adoption of the Constitution of 1787, there was no United States, just some British colonies or formerly British colonies organized under The Articles of Confederation.

[RedMDer]

They may not have thought that at the time.
Please see post 28.