This sounds like the Luftwaffe beat the Americans by several years.
Quite likely. In fact there are graded definitions creeping in (as always) and so Yeager achieved the first recorded level, controlled supersonic flight and the XP86 is recognised as the first recorded controlled flight in a descent.
It makes you wonder how many unrecorded flights there were, how many uncontrolled flights (the Swallow may have fallen in this bracket) and how many earlier penetrations of the sound barrier actually happened. There is evidence to suggest a few Spitfires may have gone supersonic but not in any controlled manner and it is likely other fast pistons, and some early jets, may have punched into the unknown.
It would be rather intriguing to know who may have really been the first to cross the boundary - controlled or not.