In 1954, Soviet rocket engineer Sergei Korolev could not get funding to pursue a space program, so he planted a fake new-story claiming Russia was going to launch a satellite. The US responded that they were also going to launch one, so the Soviets then agreed to fund the program.
During the Cold War, playground equipment in the US and the USSR was made with the intent of getting children to be interested in the Space Race.
The Soviet Union and the United States were originally in talks to go to the moon together during the Cold War. Nikita Khrushchev was poised to accept the plan but then President Kennedy was assassinated. The Soviets did not trust Vice President Johnson, so Khrushchev rejected the plan.
In a secret 1960 operation, the CIA stole the Russian satellite Lunik overnight completely disassembling, examining, and reassembling it within 12 hours, and returned it in the morning without the Russians knowing – possibly changing the outcome of the space race.
The US government planned to set off a nuclear bomb on the moon to boost morale during the Space Race.