After which Cold War event did the United States and the Soviet Union enter a nuclear arms race?

The Cold War event that sparked the nuclear arms race between the United States and the Soviet Union is usually said to be the bombings of Hiroshima and Nagasaki.

The United States wanted World War II to end, but Japan would not surrender. Instead of sending troops into Japan, which would potentially cost the lives of Americans, President Harry S. Truman dropped two atomic bombs on Japan. The two atomic bombs that were sent to Hiroshima and Nagasaki killed thousands of people but caused Japan to surrender, which Truman wanted. Finally, World War II was officially over, but tensions between the Soviet Union and the United States continued.

The Soviet Union no longer trusted the United States after the bombings of Hiroshima and Nagasaki, because even though they were allies, the United States never mentioned they had such a powerful atomic weapon. This sparked the nuclear arms race between the United States and the Soviet Union, as they both wanted to assert their dominance with powerful weapons.

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