I'm reading a book - "One Small Step: The Great Moon Hoax" by Gerhard Wisnewski, a German (the book is a translation) and I'm surprised to see he starts out not with the USA but with the early Soviet space race achievements. What's specifically surprising is that he dismantles the Yuri Gargarin space flight and shows that it's unlikely to be true:

One thing is definite: there are many aspects of cosmonaut Gagarin’s flight into orbit that do not fit together. An aviator of medium skills with very little flying and parachuting experience rises in a very short span of time to become the leading cosmonaut of the Soviet Union. His closest contacts give only average accounts of him, and no one can remember any outstanding achievements. But this aviator happens to represent all the important ideological values of the Soviet Union. From standing he leaps straight into a complete orbit of the earth before landing again at the very place where once before he had come down by parachute. He can’t describe what he saw during his flight in any great detail. And when he does mention a fact it doesn’t accord with the flight path of his craft. There is no credible film or photographic record of his entry into the capsule or of the flight. A large part of the material is either obviously faked or else produced after the event. It will be a long time before the world finds out who this Gagarin fellow really was or what he actually achieved.

(he provides a detailed rationale for all this in the book)

Some other points to note (my summation):

• Yuri likely raped a nurse in a sanatorium he was "holidaying" in, after his alleged space flight. He was caught in the act and lept from a first floor window in shame, landing on his face and breaking the skull bone just under his eyebrow. He was mentally never the same after, a known phenomenon with such types of injuries. A planned career in politics was discarded, and he died in mysterious and suspicious circumstances in a plane crash, in which he was test pilot.

• It's likely another man was the "real" Yuri, the real first man in space. Vladimir Ilyushin, a man who was "unquestionably the Soviet Union’s most famous and experienced test pilot. As a test pilot he set dozens of speed and altitude records. And also the world altitude record of nearly 30 kilometers, which he set in 1959 using a Suchoj 9 military interceptor jet. In late 1960 Ilyushin was awarded a hero of the Soviet Union, their highest military honor, for his altitude records."

• it's likely Ilyushin's space flight took place just before Gargarin's was supposed to have taken place, but that it was almost a disaster with a crash landing at sea that almost killed him. He was discovered by the Chinese and he was incapacitated in a Chinese hospital for months. Not the sort of successful "first man in space" story USSR wanted to promote.

• USSR likely sent far more cosmonauts into LEO/space than we're told and likely many of them died in the process. Two Italian men picked up communications in Russian from cosmonauts (including a female) in the months/year prior when no missions are on record, in various states of distress. Infamously one communication was in morse-code that said "SOS To the whole of planet Earth" and they could determine the message was gradually getting further and further away and weaker until it disappeared - seemingly indicating a cosmonaut was sent out to space for a one way trip.

• these things and more were fairly well known at the time. Readers Digest ran a story on the Italians interception of communications. There was quite a bit of doubt surrounding the Russian space program in western minds. But when JFK announced about putting a man on the moon, the official line was the USA believed USSR and was going to top them. And that put an end to these suspicions and they were pretty much buried in the sands of time.

It puts the "Russian Question" debunkers bizarrely always seem to fall back on in a new perspective - ie. "why would the Russians not call out America about the moon landings being fake - they must have known." The USSR also had much to hide about it's own space race activities apparently.