Final answer:
The first serious disagreements between the United States and the Soviet Union after World War II occurred over Soviet activities in Iran, with subsequent significant conflicts arising in Europe, during the Cuban Missile Crisis, and within the context of the Truman Doctrine.
Step-by-step explanation:
The First Conflicts of The Cold War
The first serious disagreements between the United States and the Soviet Union after World War II primarily occurred over events in Iran. Following the war, the USSR failed to withdraw from Iran according to an agreed-upon schedule that they had established with the British during World War II.
Soon afterward, tensions escalated further with the Soviet Union's involvement in other regions. The Soviet activities in Europe, particularly in the Eastern Bloc, resulted in uprisings and revolutions in countries such as Poland, Hungary, and Czechoslovakia, all of which were met with force by the USSR to maintain control.
In addition to Europe, the geopolitical contest extended to other parts of the world. Significant confrontations included the Truman Doctrine, implemented to counter the perceived Soviet influence in Greece and Turkey, and the close encounter during the Cuban Missile Crisis, when the United States discovered Soviet missiles in Cuba. These events conveyed the extensive nature of the Cold War, which was a struggle for global dominance featuring proxy wars, the arms race, and the race for space exploration.