So the first 8 or nine presidents (or more) were ineligible, according to your criteria. Since the US was not a country prior to 1776, any president born prior to that year could not be “natural born citizens” since their parents obviously could not have citizens of the USA at the time of the birth. If you go by the stricter criteria (parents must have been born in the USA), then most of the presidents up until 1900 were probably ineligible.
Read the clause and you will see that they grandfathered in every citizen at the time of the adoption of the Constitution to be eligible because they knew of course that none of them could have two parents in a country that didn’t exist yet.
The Constitution takes into consideration those born at the time of the writing of the constitution. It states Natural born citizens or citizens at the time of the writing of the Constitution. That was the only exception for a citizen to become president.