For one thing, the lower classes were the biggest beneficiaries of the policies of the early revolution.

Major literacy campaign, redistribution of lands to the peasants that worked them, housing policies to try to fix the slums, ration card food distribution which helped keep people from starving, free education, etc.

Politics in mid-20th century Cuba were still largely controlled by the rich and at best representatives of the professional classes, like doctors, participated as candidates representing more middle class interests. Peasants, agricultural and industrial proletariat, etc., were largely politically marginalized and had little to no education. When Fidel came to power and pushed forward a bunch of policies that benefited them, they increasingly embranced him. When the US attempted and failed to take control of Cuba through the Bay of Pigs invasion in 1961, Fidel was able to erect himself as both a defender of the poor (against rich ex-patriots) and of national sovereignty (against the US). Maria del Pilar Diaz Castanon's book Ideologia y Revolucion: Cuba, 1959-1962 argues that through a combination of intelligent policy and the evolution of domestic and foreign factors, Fidel was able to fuse the concepts of patriotism and revolution together among many of the poor.

Economic immigration among the poor didn't start until rationing and government economic experiments had worsened the domestic situation in the 1970s, leading to the Mariel Boatlift in 1980, when poor people started to flee for a better life in the US. The difference being, now their economic wellbeing was being affected.

The Sovietization of the 1970s, both economically and in terms of education and cultural policy, had also alienated a lot of people. The government was more closed minded and dogmatic than ever and centralization in all aspects of life had gotten to a ridiculous highpoint. This was not true of Cuba pre-1968 and especially pre-1971, when the Sovietization began in earnest.