I think they went, I think the landers & rovers are still there, but IMO the rocket bit is staged (no pun intended) because it's just not doable.
Remember the "flying disc" program went "black" in 1956 ?
That's how I think they got there, as for Kubrick making the footage, highly likely IMHO, it's just not that easy to do something and film it in real time (even harder in spacesuits) , this was important & had to look good, they also didn't want any cameos by beings that shouldn't be there lol.
Black program saucers;