Hold up a soccer ball in front of you. It’s a spherical object that you could perceive as a flat, circular plane. You could just as well be holding up a plate.
How do you tell it’s a sphere? One thing you might do is just rotate it a little in your hands. No spinning, just rotate your wrist a little while the ball sits on your hand.
It will look a little like this, a sequence of photos during a 29ish day lunation.
This is lunar libration. Objects in orbit are rarely perfect nor circular. This shows how we can see a little more than 50% of the moon each month.
This can be observed by anybody. No NASA conspiracy required.