Just also putting things into context, the Moon was reached for the first time at the very end of 1968 (by humans) and the landing was 1969.
One of the great science fiction films of all time, possibly one of the great films of all time, was released the year before ie before we had even landed on the Moon. I speak of 2001: A Space Odyssey.
Now, you can look back on this film and highlight mistakes (the colour of the Earth seems a bit pale, for example, and the walking on the Moon seems wrong – a bunny hop seems more approriate), but we know director Kubrick was a stickler for detail and believeability.
I am never sure what the title has to do with anything. It is not clear what part of the film, if any, takes place in 2001. The only indication of a time is one caption, for 18 months later. I have always suspected that the date was chosen not as part of a realistic prediction of where space exploration would be, but simply as the first year of a new millennium, a fresh start to history.
Space travel is nowhere near that depiction in the film. Easy shuttle flights to a space station, bases on the Moon, suspended animation and missions to Jupiter are just as far off now as they were then, disappointingly.