Maybe have America be somewhat less sane in foreign policy. IOTL, we made it clear early on that we considered right-wing strongmen like Batista just as abhorrent as communist regimes.
Cuba is 130 miles off the south coast of Florida. The United States would never tolerate a nation that close to its borders that was hostile; the most 'hostile' that would ever be tolerated is a militarily neutral country with sympathetic trade concessions - a Finland with palm trees.