As a Cuban born during this time, all it would have taken for Cuba to fall is supplying arms and food to Cubans to get them to overthrow the government. El Periodo Especial was a really bad time in Cuba, people being fed fried up mop as a meat substitute comes up as one grim example of how bad it was.
The utterly meagre rations the government provided could not possibly feed a healthy adult and the black market flourished. My father had to ride his bicycle past provincial guard posts in the mountains in order to get produce and eggs straight from the source.
Another thing that would have toppled the govt, would have been if the Cuban government was struck with another case of stupidity and actually attempted to crack down on the black market and up the amount of chivatos on the streets. However, the ripest time for such a change would be between 1990-97 and especially 1992-95 which were the three harshest years.
A much more bloody Maleconazo could also have been the spark of outrage that would have brought down the first order just the thing to spark an uprising.
In all honesty w/o a case of actors acting in their interests or a POD before 1990, there's no real chance of the Cuban government collapsing. It had nearly 40 years of experience of maintaining power, and the Cuban govt was always more realistic and cynical than the Soviets ever were in those terms. Hell, Glasnost and Perestroika were outright condemned from the get go. As always, Cuba was politically ahead of the curve in its Warsaw-era interactions.