Final answer:
The Cuban Missile Crisis of 1962, a standoff between the US and the Soviet Union over nuclear missiles in Cuba, prompted the creation of the Big Creek Missile Agency.
Step-by-step explanation:
The event that prompted the creation of the Big Creek Missile Agency was the Cuban Missile Crisis of October 1962. This crisis was triggered by the discovery of nuclear missiles in Cuba by American intelligence.
The confrontation between the United States and the Soviet Union brought the world to the brink of nuclear war. Both nations had their long-range bombers on standby, ready to launch nuclear missiles.
The crisis ended with the installation of a direct communication link—the 'hot line'—between Washington and Moscow and led to the signing of the Limited Test Ban Treaty of 1963.