There are several problems, one being...
that Kubrick was working on movies while he was suppose to stage Apollo missions.
Anyways, lets do some calculations: 2001 lasted 2.5 hours and took 2 years to make.
The EVA of Apollo 11 lasted about 2.5 hours. It came out in 1969, so had to be finished by 1967. That would mean 2001 had to be finished by 1965.
Apollo 12 had a total EVA duration of 7 hours and 45 minutes, so would take about 5 years to make. It would need to be finished in 1964
Then: Apollo 11 had to be finished in 1962
And 2001: 1960
But shit, then Kubric was working on Dr Strangelove, Lolita and Spartacus
I guess we should push the dates further back? Oh but shit, then he was kind of making a movie every 2 a 3 years, working on Lolita(1962), Spartacus(1960), Paths of Glory(1957)
So when did Kubrick have time to stage all of NASA's footage?
Of course I didn't take into account All pre-Apollo 11 footage, and non-EVA footage into account. That had to be staged too. Nor did I go further than Apollo 12, because as you can see, it will only make things worse. Given those mission EVAs lasted +10 hours.