The US failed missions such as the Bay of Pigs and Operation mongoose. They also placed Missiles in Turkey and Italy, and quarantined Cuba. The USSR had Sputnik which gave the Us reason to believe the Soviets could hit them, and also scared the American Population. They also put Missiles in Cuba. But what actions did Cuba and Castro do that influenced the CMC? Besides the obvious "they accepted missiles from the Soviets". I have always pondered this. Thank you for your help /r/AskHistorians !
The Cubans were extremely skeptical from the start with the amount of force the Soviet Union claimed that they could get into the island. As Richard Gott discussed in his book Cuba: A New History, 42K troops, 50 aircraft, 12 submarines, and dozens of conventional and nuclear missiles would be brought secretly into Cuba. Cuban questioning was simply waved away with the Soviets citing their "expertise in such matters." The Soviets seemingly went all out trying to prove their prowess in such matters with military hero Marshall Sergei Biryuzov taking Raul Castro on a tour of the island. Biryuzov explained how and where the missiles would be placed, explained how the new equipment would function, and discussed the amount of Soviet troops that would be need accommodation. It seems the relationship was the Soviets telling the Cubans how it was going to be. Taking another quote from Gott's book, Fidel seemingly laments being left out of the loop after the United States' discovery of the missiles with "If we had known what those missiles were like and if the question of camouflage had been posed to us, it would have been easy to decide what to do."
The negotiations to end the Crisis went over the Cubans head, with President John F. Kennedy and premier Nikita Khrushchev discussing them without any input from Cuba. This lead Ernesto Guevara, who, along with Raul Castro, largely built the relationship with the Soviet Union, to begin denouncing the USSR almost as frequently as the United States. Jon Lee Anderson really drives this home in his book about Guevara, wherein the iconic revolutionary laments that the missiles were not in Cuban control, because they would have used them.
This caused a strain on the relationship between Cuba and the Soviet Union with the Castro brothers fighting Soviet influence from without and within while still attempting to get help from the Soviet Union as a fellow communist country. In Cuba, Castro, and Revolution, editied by Jamie Suchlick, a quote from the Soviet military paper Red Star defines what Cuba hoped for; “guided by its international duty and a feeling of fraternal solidarity, the Soviet Union has given, is giving, and will continue to give socialist Cuba comprehensive help in strengthing its defense capabilities.” Though, that's really a different discussion entirely.
TL;DR It seems that once the Soviets were allowed into Cuba, Cuban involvement in what happened next disappeared. Guevara seemed to be right in his assessment that the Soviet Union was just using Cuba as a pawn.