The US doesn't like a new leader (Castro) who overthrew an old client of ours (Batista's Cuba). New leader listens to his brother and friend (Che) about looking to another power for support (USSR). We dislike it, and the CIA and DoD plan a sneaky way to overthrow the shaky government. We train and supply 'rebels' to land in Cuba and fight Castro's men. They will inspire a popular uprising, sweeping the shaky leader out in a counter-revolution. This failed miserably because Castro had spies in the exile camp. The Cuban uprising was a CIA lie that pushed our leaders into supporting the effort, and President Kennedy neglected to use air power to support the rebels. History shows Castro repels the exiles, solidifies support, and at last check, he and his cronies are still in power. America just picked up the pieces and worked on the regime toppling formula.
The motivation sounds the exact same as today but our methods are different. The US is still stupid enough to think popular risings will help (Iraq). We also always look for the cheapest way possible to topple a regime. The US has a compliant media that will report on atrocities of the target leader or group. Asymmetric warfare and mass production of high powered rifles allow for arming insurgents easier. Most importantly, the US has completely abandoned any pretense to respecting the Westphalian concept of sovereignty, and we will use our supreme differentiator to tip the playing field towards our friendly insurgents, airpower. A no-fly zone works wonders to destroy the major advantage a state has over insurgents in military capabilities: air power. Ask Saddam and Qadaffi in hell. The Bay of Pigs wouldn't happen today because it'd be an uprising started in metro centers. The US would lead the international enforcement of a no-fly zone, and Castro would be gone. I'll amend my initial statement. The clowns' motives and antics stay the same, only the location changes.