Separately from the elite's contact, the major militaries are aware of the defense threat of having aliens around with higher technologies. So we each have a covert space program, because it is mandatory to have some defense effort. We use captured alien craft to advance our capabilities. We may have covert bases at the poles maybe inherited from the Germans, and of course Nevada and New Mexico.
At the same time we have a public-facing space program which is of inferior capability but hey, the sheep are stupid. I believe we were already in space before the (inferior technology) shuttles were shut down.
Chances are very good we're on the moon and probably Mars.
Some of the missing budget trillions are tied up with all this (though a lot is in DUMBs built as backups for catastrophe and invasion. DUMBs will live through a mag pole reversal and ensuing radiation).
I think the full game is a bit complicated.