Relations between USA and USSR were bad and had been worsened by the U2 incident in May 1960. Cuba was an island only 90 miles from the coast of Florida and in the Military base at Guantamano within it had been leased by USA to USSR for 99 years.
In the 1930s Cuba had been under the rule of the military dictator Batista. He was supported by the USA and allowed American Businessmen to make huge profits from plantations and business in Cuba. There was a huge different between rich and poor and most Cubans lived in poverty. Under Batista Cuba became bankrupt.
In 1958, after a fairly lengthy conflict, Fidel Castro overthrew Batiste’s government and on 1st January 1959 formed a new government with himself as ruler. Castro wished to free Cuba from American influence. He began to nationalise American industries in Cuba and approached communist countries for money. The USA broke off any relations with Cuba and refused to buy anymore sugar, Cuba’s main export.
The only country willing to help Castro was Russia. It bought the sugar crop and supplied the island with oil. Castro’s views now became more communist and Cuba fell under soviet influence.