Note the reference to Natural Law in the first sentence of our Declaration of Independence.
It is crystal clear that the Founding Fathers used the Natural Law definition of 'natural born Citizen' when they wrote Article II. By invoking "The Laws of Nature and Nature's God" the 56 signers of the Declaration incorporated a legal standard of freedom into the forms of government that would follow.
President John Quincy Adams, writing in 1839, looked back at the founding period and recognized the true meaning of the Declaration's reliance on the "Laws of Nature and of Nature's God." He observed that the American people's "charter was the Declaration of Independence. Their rights, the natural rights of mankind. Their government, such as should be instituted by the people, under the solemn mutual pledges of perpetual union, founded on the self-evident truth's proclaimed in the Declaration."
The Constitution, Vattel, and “Natural Born Citizen”: What Our Framers Knew
The Supreme Court of the United States has never applied the term “natural born citizen” to any other category than “those born in the country of parents who are citizens thereof”.
Citizenship Terms Used in the U.S. Constitution - The 5 Terms Defined & Some Legal Reference to Same
"The citizenship of no man could be previous to the declaration of independence, and, as a natural right, belongs to none but those who have been born of citizens since the 4th of July, 1776."....David Ramsay, 1789.
A Dissertation on Manner of Acquiring Character & Privileges of Citizen of U.S.-by David Ramsay-1789
The Law of Nations or the Principles of Natural Law (1758)
The Laws of Nature and of Nature's God: The True Foundation of American Law