From a presidential perspective, the United States will only launch if they feel the Soviet Union is poised to immediately launch, and the US fears that their nuclear capabilities will be wiped out so they will not be able to retaliate at full strength. Bear in mind that under Eisenhower, field commanders still had the ability to use atomic weapons at their discretion. So a field commander could start WW3 if he sees fit, which was a problem. Kennedy inherited Eisenhower's Joint Chiefs of Staff, who were very militant, but whom Kennedy did not feel comfortable getting rid of, lest he be seen as an ignorant, naive blue blood who was undermining the wisdom of the man who won World War 2. His plan was to slowly ween them out of the government and to replace them gradually. On the whole, Kennedy was horrified and disgusted by the Eisenhower administration treatment of atomic war, especially the plans of the Joint Chiefs in this regard. Eisenhower tried to impress president elect Kennedy at the White House by calling up his helicopter and showing how fast it would arrive to evacuate. Kennedy was not impressed, because in his view, if you had to evacuate because atomic exchange had engaged, you had already failed. The Joint Chiefs actually refused to turn over their plan for an atomic war to Kennedy until they were pressured to do so by the administration. The plan was a wholesale genocide, and in disgust Kennedy remarked "and we call ourselves the human race." Kennedy instituted a lot of reforms to the possibility of nuclear exchange.
There is a world where there was no reform, and there remained a disconnect between the president and the Joint Chiefs on atomic warfare. The president would exist in a benign ignorance, and the Joint Chiefs would have carte blanche to do as they thought best. And that is a world where nuclear exchange is a very frightening reality. If Eisenhower had overseen a quagmire situation like the Cuban Missile Crisis, which was a very real possibility to occur somewhere at sometime in the world, I honestly believe there would have been a nuclear war. Already, Eisenhower advised the President to move in with military force on Cuba, and his reaction to the possibility of the Soviets moving into West Berlin was that they simply would not. We know now they would have, and would have greeted American troops on Cuban beaches with tactical nuclear weapons which the US did not know were already active there. So that thinking could have been brought in anywhere in the world, and the story would always be American troops move in, likely get greeted by Soviet forces and tactical nuclear weapons, and the Soviets move into Berlin and there are zero minutes to midnight. The early 1960s were actually a very frightening time in regards to how close we could have come to the brink if it were not properly negotiated and treated with a nuanced, careful approach.