Cuba had been an unofficial colony of the US since the end of the Spanish-American War. While independent, America had a lot of influence over who was in power, what their policies were, and more or less used the island as a business and social playground.
During the war years in the early 1940s, Fulgencia Batista was elected fair and square, and adopted a new Constitution that was pretty generous to workers and peasants alike in terms of rights and policies.
That didn't translate to a better life for most Cubans, who worked in the tourism trade in the cities, or as farmers for large landholders on the old Spanish plantations, where they scraped out a living.
Cuban government in those years was notoriously corrupt, so even when a policy was beneficial on the surface, most times the money for those programs was siphoned off or stolen.
So in summary, average Cubans were poor, with rich family lives and traditions, but little chance for prosperity.