So apparently you missed the part where the majority of Cubans supported the Cuban revolution and also.....would protest when Castro pursued lighter sentences during the trials of the Cuban revolution.

Also....the whole reason for the failure of American attempts to overthrow Castro such as the Bay of Pigs was due to popular support that Castro had. The Office of the Historian in the U.S State Department explicitly states as such in their official records when speak about the reasons for why the Cuban embargo had to be put in place.

"Salient considerations respecting the life of the present Government of Cuba are:
1.
The majority of Cubans support Castro (the lowest estimate I have seen is 50 percent).
2.
There is no effective political opposition.
3.
Fidel Castro and other members of the Cuban Government espouse or condone communist influence.
4.
Communist influence is pervading the Government and the body politic at an amazingly fast rate.
5.
Militant opposition to Castro from without Cuba would only serve his and the communist cause.
6.
The only foreseeable means of alienating internal support is through disenchantment and disaffection based on economic dissatisfaction and hardship.
If the above are accepted or cannot be successfully countered, it follows that every possible means should be undertaken promptly to weaken the economic life of Cuba. If such a policy is adopted, it should be the result of a positive decision which would call forth a line of action which, while as adroit and inconspicuous as possible, makes the greatest inroads in denying money and supplies to Cuba, to decrease monetary and real wages, to bring about hunger, desperation and overthrow of government."_Deputy Assistant Secretary of State for Inter American Affairs Mallory(April 6, 1960 Memorandum)