I’m an amateur historian, but I am in law school so I think my answer would be suitable here. The key here is to read the rest of the phase you have put forth.

“We the People of the United States, in Order to form a more perfect Union . . . and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.”

Here, it refers to pretty much anyone who was not a slave and Dwelling in the country at the time of formation, not just LIVING there, and also people who become citizens of the U.S. through naturalization. For instance, Alexander Hamilton was born on a island in the Bahamas. Under normal circumstances he would not be considered a natural born citizen, but because he dwelled within the colonies before the formation of the country he was considered a “natural born” citizen. Which is why he could’ve ran for president even though he wasn’t born in the United States; no one was born in the United States at that time because the United States technically didn’t legally exist for them to be born in!

This isn’t to say however that every citizen had equal rights (as I’m sure you well know).

Also, the term “Posterity” here means any of the future generations of the Citizenry (their kids).