The Superman comic book premiered in 1938. So, the latest toddler Kal-El could have landed in Kansas was around 1920. Long before the advent of SSN assigned at birth. And at a time when most children in rural farming country were likely born at home. And rural farmers wouldn’t be hurrying into town to register such births. Not unless they were going to town already. So no one would question where this kid came from. Not then in small town Kansas.

Also, from comic book canon, Superman revealed his origin to President Eisenhower. Ike told him not to worry. “It’s not like we can deport you. Krypton no longer exists!” The implication was that Ike guaranteed his American citizenship would never be challenged.