Re: New President -
"A person of unknown parentage found in the United States while under the age of five years, until shown, prior to his attaining the age of twenty-one years, not to have been born in the United States"
Unless someone supplied proof of non-citizenship of Superman by Supe's 21st birthday, he would be considered a natural born US citizen and be eligible to be elected or appointed POTUS.
This is discussed under Title VIII - Chapter XII - Subchapter III - Part I - Section 1401 - Paragraph (f).
P.S. It would not require a constitutional amendment, but merely a change in law.