This is an interesting question on several levels. The Cuban Missile Crisis took place from October 16 through October 28, 1962, when the United States confronted Cuba and the Soviet Union with a naval blockade over newly constructed ballistic missile facilities on the island. The year before, anti-Castro Cubans supported by the United States took part in an ill-considered, poorly and naively planned, and incompetently executed counter-revolutionary invasion of Cuba at the Bay of Pigs. Cuban dictator Fidel Castro requested the Soviet Union's assistance with missiles in order to protect against any further invasion, which led to the naval blockade.
That said, under Castro's regime, thousands of Cubans had their property expropriated and livelihoods destroyed, and thousands of other Cubans were imprisoned, murdered, and "disappeared." Even though Cuba ostensibly has universal education and health care, it is apparent from journalistic reports that even today, Cubans criticize their government at their peril. More importantly for United States's national security interests, Cuba's very able military and intelligence services have fomented and supported revolutionary movements throughout Latin America, and they continue to do so in places such as Venezuela.
Therefore, this question could easily be rephrased to ask to what extent the excesses of the communist government of Cuba made confrontation with the United States inevitable.
A more neutral question to ponder is the best way for the United States to address such a destabilizing element 90 miles from its shores, since neither a trade embargo nor UN influence have been effective at bringing about positive change.