What incident exposed the Soviets' military inferiority and led to the buildup of weapons in the United States and the Soviet Union?

The Cuban missile crisis

Explanation:

The Cuban Missile Crisis also known as the Missile Scare or Caribbean Crisis, happened in October 1962. It was a 13 days dangerous confrontation between the United States and the Soviet Union over the arrival of Soviet technicians with equipments to manufacture Soviet nuclear-armed missiles in Cuba.

President John F. Kennedy on the 22nd of October announced the a naval quarantine to stop the delivery of missiles and demanded the existing missile sites in Cuba be dismantled immediately.

The Cuban missile crisis exposed the Soviets' military inferiority and led to the buildup of weapons in the United States and the Soviet Union.