How successful were the USA and USSR in showing their dominance over the other?

The two sides decided to use other countries to fight for them, for example: they fought each other’s allies. The US fought against North Vietnam, a pro-soviet country in the Vietnam War. They helped their allies to fight each other. For example, the USA backed Israel and the Soviet Union backed Egypt in the wars in the Middle East. They gave help to opposing sides in civil wars.. The Americans used armed force to get rid of pro-soviet governments in countries close to the US, such as Cuba. The Soviet Union used armed force to stop rebellions against pro-soviet governments in nearby countries such as Hungary. As tensions were rising, so was the competition between the two countries. One seemed to follow the other in the exact same way, for example: The arms race: 1952: the USA exploded its first H-bomb and started building long-range bomber aircrafts. In 1953, in the same way, the Soviet Union exploded its first H-bomb and started building long range missiles. In 1980’s, US began work on ‘Star Wars’ satellites which use laser beams to destroy incoming Soviet missiles. Again, Soviet researches experimented with particle beams to destroy incoming American missiles. In 1948, the USA gave $16 billion of aid to European countries to stop the spread of communism into Western Europe. In 1960, the Soviet Union started giving money and arms to the new anti-American government of Cuba.  It can be deduced that the US lead the way in terms of taking action with the Soviet Union following closely behind not wanting to be overshadowed and dominated by the US.  The US President Roosevelt died in 1945. He was replaced by Truman who was strongly anti-Communist and, as the war came to an end, the stop the Vietcong guerrillas. Eventually had to retreat from Vietnam achieving nothing. When Castro came to power, however, he nationalised American companies in Cuba. In retaliation, the Americans stopped all aid to Cuba, and all imports of Cuban sugar. This was a blow to Castro as sugar was the mainstay of the Cuban economy. Castro was forced to look to the USSR for help, and, in 1960, the USSR signed an agreement to buy 1 million tonnes of Cuban sugar every year. Castro, who had not been a Communist when he took power, became a Communist. They finally got weapons, very close to USA, could have destroyed America, missiles from Russia.