"Dial of Destiny" is set in 1969, and part of its backstory involves the Apollo 11 moon landing. It is stated that the main villain of the film, Jürgen Voller (Mads Mikkelsen) — who goes by the much less conspicuous name "Dr. Schmidt" — is a former Nazi scientist scooped up by the United States government at the end of World War II to help build rockets for NASA.
This is based on a real US government program called "Operation Paperclip" (via history.com), also mentioned briefly in "Captain America: The Winter Soldier." Essentially, during WWII, German scientists developed V-2 rockets, some of the most advanced at the time. Afterwards, once the Nazis surrendered, their tech, scientists, and research were all up for grabs.
Although "Paperclip" was originally launched to stop German scientists from taking their research to other potential enemies, the US soon began a decades-long Cold War with former ally The Soviet Union; "Paperclip" served as a scientific advantage for the US, helping significantly with getting a jump on the so-called "Space Race." Over 1600 scientists, as well as engineers and technicians, came over from former Nazi Germany, many given lucrative jobs. Many of these scientists worked for NASA, many on multiple Apollo missions — including Apollo 11, as seen in the film. Although some played central roles in developing things like space suits, the Hubble telescope (including Ernst Stuhlinger, pictured above) and the Saturn V launch vehicle — which made human missions to the moon possible — multiple Paperclip scientists would later be investigated and/or disgraced over their ties to the Nazi Party.
