On Tuesday April 1st 1980 Hector Sanyustiz and 3 others drove a bus into the fence surrounding the Peruvian Embassy in Havana. The Cuban guards opened fire on them and wounded one but the others made it into the embassy safely and asked for political asylum. The peruvian ambassador granted it. Fidel Castro flew into a very public rage and demanded that the Cubans be returned. When the Peruvian ambassador refused to do so Fidel made, as far as I know, his first public misstep in full view of all of Cuba.
Fidel appeared on every radio and TV station in Cuba with one message, he said that unless the Peruvian ambassador returned the asylum seekers he would remove all Cuban protection from the embassy, and he would not be held responsible for what happened after that. He was in fact inciting the Cuban people to storm the Peruvian embassy and grab the defectors. He was half right.
On Friday April 4th, Good Friday, word spread through Havana that the guards around the Peruvian embassy had been removed. Within hours 10,000 Cubans had stormed the Peruvian embassy, but instead of grabbing the defectors they had instead asked for political asylum. Fidel was further enraged, but he would only compound his mistake by his next actions, he went on radio and TV again and said that anyone who wanted to leave was free to do so, and to gather at the port of Mariel for processing. In a few days over 100,000 people had gathered there.
You probably know some of what happened next, to offset his embarrassment Fidel took some of the worst criminals and mental patients and mixed them among those wanting to leave, then pointed to those as typical of who wanted to leave. But he was wrong, and this very public embarrasment was the first sign for those in Cuba that 1. the regime was not as strong as it seemed, and 2. there were a whole lot of people who were completely dissatisfied with the regime, even if they’d never said so.