amateur observing - What is the first recorded reference to the Moon being a satellite of the Earth?

From before the dawn of history people naturally assumed that the sky was a solid dome above the flat earth. The dome was assumed to rotate once a day, so the stars were assumed to be lights attached to the dome.

Anyone who assumed that the sky dome was opaque had to assume that the sun and the wandering planets were nearer than the sky dome. I think that it was usually assumed the sky dome was opaque and colored blue, thus making the sky seem blue when it reflected the light of the sun during the day, thus making the sun closer than the sky dome.

Those who kept records of astronomical observations soon noticed that the moon occulted or passed in front of stars, planets, and the sun (solar eclipses), and thus was closer.

Everyone assumed that the sun and the moon were tiny, until traveler's reports showed that they had the same apparent diameters every place that as visited, and so were about equally far away from every place that was visited. Thus as the size of the known world grew larger and larger, the minimum possible size and distance of the moon and the sun grew larger and larger.

The idea of a spherical earth was proposed and gradually accepted by Greek philosophers between the sixth and third centuries BC. Thus the earth became known as Earth, a sphere instead of a flat disc, and the dome of the sky became a hollow spherical shell around it.

In Hellenistic times the diameter of the Earth was calculated with reasonable accuracy, as well as the distance to the moon and thus its diameter. So it became known that the moon was about a quarter the diameter of the Earth and over sixty Earth radii distant.

Because of solar eclipses, it had been known since prehistoric times that the moon was closer than the sun, and keepers of astronomical records of events when the moon occulted (passed in front of) stars and planets knew that the moon was closer than planets and stars.

Anyone who assumed geocentrism, that the Earth was the enter of the universe, naturally assumed that every object revolved around the Earth, including the moon, and that the moon was thus the closest satellite of the Earth. A few ancient Greek philosphers supported the Heliocentric theory, that the Earth and the planets revolved around the sun. Some of them could have believed that the moon also revolved around the sun, but as far as I know all heliocentric believers also had the moon revolve around the Earth.

By the last few centuries BC there were many educated persons who believed that the Earth, the moon, and the sun were giant balls of rock (and thus somewhat similar objects), that the sun was a giant burning rock, and that the stars and planets might also be giant burning rocks far, far away from the Earth and appearing as dots as seen from Earth. Since everybody already since prehistoric times believed that the moon revolved around the Earth, by the last few centuries BC educated people in Western civilization believed that the moon was what we now call a natural satellite of the Earth, though some of them believed and some did not that the sun and planets were also natural satellites of the Earth.