While the USSR flushed the seas with incredible numbers of submarines, in the US one Hyman G. Rickover pushed the navy into going nuclear and set up USS Nautilus to become the first submarine to traverse the North Pole submerged. Meanwhile, the Soviets had their own breakthroughs - ICBMs, SSBNs, SLBMs and, of course, Sputnik. But opposite that the Americans set up SOSUS, a revolution by itself.
For more in Hyman G. Rickover, see Hyman G. Rickover, Father of the US nuclear navy (ahistoryofsubmarines.com).