Aha, I misread miles as kilometers (probably thinking of the von Karman line at 100 km, generally recognized as the edge of space by international organizations).

Several X-15 pilots eventually got astronaut wings for passing 50 miles, but only one of them (Joe Walker) actually flew above 100 km. It was after several people had been in orbit, but his Wikipedia page calls him "the first man to fly into outer space on two different occasions".