If you unironically have fallen for the flat earth CIA psyop, there is one easy experiment you can do to prove yourselves wrong.
Step 1: buy GPS enabled go-pro
Step 2: buy high altitude capable balloon
Combine the two, watch the balloon go up, track where it lands, watch the footage for yourself and free yourself from Mockingbird bondage.
For a little extra, you can configure a live feed system and watch everything in real time all under your control! Yes, it really is that simple!!!
I've helped build a space ship and sat in mission control while it orbited in space, and watched video of it and the Earth streaming from it through radio equipment that I helped build. If it was fake, they fooled me.
The moon always faces the Earth because of "tidal locking". Because of the Earth's gravity pulling on the moon, earlier in history when the moon did spin more often than it orbited the Earth, the moon experienced tidal forces. Those forces caused the moon to constantly change shape elliptically, and dissipated massive amounts of heat. Heat is energy, and that energy came from the moon's rotation. Eventually the moon ran out of rotational energy and became in synch with its orbit. The Earth is gradually slowing down over time as well, which is why a leap second gets added every few years to UTC. There are actually a bunch of moons orbiting other planets that are tidally locked to their planets as well. It's more common than not I believe.
Without getting into the universe expanding, 66,000 MPH isn't very fast at a cosmic scale. Going 66,000 MPH for 10,000 years would get you about 1 light year. The closest star from our sun is about 4 light years away. Our galaxy is about 100,000 light years wide. Stone tablets and cave drawings wouldn't have the necessary precision to notice the subtle changes in constellations over the years.