When Castro's 26th of July Movement overthrew the Batista regime, Cuba had long fallen out of good graces with Washington, and had essentially been cut loose. The movement had made no outwardly communist genuflections to avoid any reinforcement to Cuba, and were able to take advantage of widespread discontent among the institutions of state as well.
There is never any analogue to this ITTL. The exile regime in Cuba enjoys the support of the UK in the 30s, who are using it as a major naval anchorage and a staging point for the RAF to contest the Carribean. MacArthur is financially supported, ensuring that at the very least the soldiers and Cuban elites are going to get their due. By 42, the native communists are instructed to support a Popular Front for the war effort. They enjoy a very brief period where they're not mercilessly suppressed, and are suppressed quite ruthlessly again in 1948, with many leaders, with a false sense of safety, are rounded up very quickly. The FBU continues to use Cuba as a major military staging area, including nuclear missiles, bombers, submarine pens, and an army garrison. An exile community, several hundred thousand strong, and some recent FBU transplants, are increasingly marrying into the White Spanish Cuban elite. Many will proudly call themselves Americanos in thickly Spanish accented English.
The peasants are kept in line. The workers are suppressed. The elites continue to enjoy the luxuries of their class, and the FBU will not give up such a strategically valuable position.