We are of course talking about an undefined term that appears in the constitution for political purposes. My thinking is guided by the political situation in 1787. The Convention devised an office that was unique at the time. The holder of that office would not be a sovereign but a chief magistrate who might have been called a governor-general. He would be George Washington and he would not be a foreign prince. Those were two effective ways of avoiding the establishment of a monarchy to succeed that of George III.
That he had refused to act the part of Cromwell and that he had no natural heirs more or less sealed the deal.
It has been defined many times by many reputable legal sources and by the common law of England. Natural born citizen means born under the jurisdiction of a sovereign and into the allegiance of the same. It means native born. It means born on soil owned and/or controlled by the sovereign. Its meaning was well understood at the time the constitution was adopted. The meaning has been forgotten perhaps over the centuries but it was not lost.