Foundlings have their own specific section much further dsown.
(7) Foundlings . Under the Nationality Act of 1940, a “child” of unknown parentage , if found within the United States after January 12, 1941, and before December 24, 1952, was presumed to be a native-born citizen until shown to have been born outside the United States. 13/ A “person” whose parentage is similarly unknown, if found in the United States after December 23, 1952, while under 5 years of age, is conclusively presumed to be a native-born citizen, unless such person’s birth outside the United States is established before he or she attains majority. 13a/ Prior to Nationality Act of 1940, the statutes contained no provision governing the status of the founding. 14/
It’s the first spot on the page you linked to that specifically uses the term “native-born.”