Except the phrase “Natural Born Citizen” didn’t appear in any translation of Vattel until 10 years AFTER the Constitution was written, and it is a poor translation of what he wrote, which was - if one just transliterates - ‘the natives, or indigenous’.
Pretty hard for the Founders to use Vattel as a legal dictionary for NBC when Vattel didn’t HAVE NBC until AFTER the Constitution. Had they relied on Vattel for their legal term, they would have required the President be a “native citizen”...
You keep repeating the same debunked nonsense. Vattel wrote about natural citizenship occurring at birth. There’s no other way to translate that other than natural born citizen. Second, the Supreme Court had no problem with the translation and saying that it WAS the nomenclature known to the founders.