The Apollo program was run in the midst of the Cold War during the space race between USA and Soviet Union.
The space race was a tight competition between the Soviet Union and the United States, with both sides aiming to gain a political and military advantage over the other. If the Russian government had a reason or a proof to demonstrate that the lunar landing was fake, it would surely have exploited the opportunity to discredit NASA. During the Cold War and space race, the Soviet government monitored the United States' technological developments closely, and would very likely have noticed inconsistencies between these developments and what the States claimed to have achieved. According to Russian cosmonaut Alexei Leonov, Soviet party leaders immediately sent a letter of congratulations to the USA for their achievement, and only blamed their own program for lack of resources. Even today, Russia continues to commend the United States for putting the first man on the moon - Dmitry Rogozin, the director-general of Roscosmos State Corporation for Space Activities, congratulated NASA on the 50th anniversary of the moon landing in July 2019. If the Soviet Union had any reason to believe the moon landing was faked, they would not have gone to such great lengths to congratulate the United States on its achievement.
The Soviet Union was mostly tracking the development of American military technology, such as missiles and the atomic bomb; spacecraft were not the main focus. The United States, therefore, would probably have been able to get away with faking a moon landing and hiding it from the Soviets.