That's not how it works, before Batista's coup, the president was Prios Socarras, that had no beef with the US, I would say the opposite. Batista's coup, was an inside job. https://en.wikipedia.org/wiki/Fulgencio_Batista#Military_cou...
Batista was losing to a left-wing candidate, did a coup, and there was no election. Then he continued to support US corporate interests. This doesn't track at all with, you know, *gestures broadly at US intervention in Latin America* to you?