Many wartime planes went supersonic in a dive. Few survived to tell of it though.
The plane that finally did it in peace time was the Miles M52, well it WOULD have been the Miles, except the total plans for it were handed to the USA and UK government funding withdrawn from the Miles company. It appeared virtually unchanged as the Bell X-1 , with American stickers all over it. But it was in essence the Miles plane. A smaller unmanned version of which had reached Mach 1.38 in about 1946/7.
The key thing that allowed the X-1 to maintain control in transonic flight was the Miles' all moving tailplane. This got around the control reversal that plagued transonic aircraft fitted with conventional elevators.
The USA was about 5 years behind everyone else in jet engines and high speed flight, till they lifted what they could from the UK and Germany to make up for the ideas and research they didn't have. Of course staying out of the war as long as possible, lending money to the winning side, finally joining it, and not actually ever getting bombed proved excellent business, and they were then the only country in the world with enough money left to spend on waving a supersonic dick around.