There also was caution on the side of the USA. President Eisenhower was being urged to launch a nuclear strike against the USSR by the Secretary of the Navy, but instead decided to begin the U-2 program to see what the Soviets were up to. That showed him that, in fact, the Russian were not preparing any kind of invasion or launching of missiles. My Dad was the leader of one the teams that developed the cameras for the U-2.
In the incident with the nuclear submarine that was being bombed by an American battle group in the Cuban Missile Crises that decided not to launch a nuclear strike to protect themselves--in that incident the person that voted not to strike back against the Americans was promoted to admiral.
The other incident in which the officer was ordered to launch missiles against the USA if he saw a missile launch against the USSR, and he decided not to launch, I think he was demoted. (He had seen only one missile on the screen, and decided it was a computer glitch.)