From Wikipedia, Alan Shepherd, first American in space:
Unlike Gagarin’s 108-minute orbital flight in a Vostok spacecraft three times the size of Freedom 7,[71] Shepard stayed on a suborbital trajectory for the 15-minute flight, which reached an altitude of 101.2 nautical miles (116.5 statute miles; 187.4 kilometers), and then fell to a splashdown 263.1 nautical miles (302.8 statute miles; 487.3 kilometers) down the Atlantic Missile Range.[79]
I get your point, and Alan Shepherd is my own personal hero (absolutely inspiring how he came back from Menier’s to go to the moon). I don’t count his suborbital either, but he had a serious pair getting in after all the booster failures.