What evidence do we have that the moon has been here throughout Earth's history?

well other than science our biggest proof is human documentation. Civilizations have been documenting the moon for centuries through pictures and drawings. You can write that when you go back in time, the documenting of the moon isn't there at a certain point in time.

Humans began to practice sedentary agriculture about 12,000 years ago so I'm pretty sure the moon existed 12,000 years ago.

But other than human documentation you would have to rely on science. There are nocturnal creatures that depend on the moon. You would need to write about these animals not existing at a certain period of time the moon "didn't exist" Then, you would also need to write about the tides. The moon is responsible for the changes in the earth's tides to, with tides being weaker you would need to write about how that changes the ecosystem that relies on those tides as well.

You would also need to talk about how the changes in atosphere and air circulation of the earth would be like, without a moon our environment would be closer to jupiter.

All of the evidence indicates that the moon was formed several billion years ago when a small planet collided with the earth.

http://www.space.com/18106-moon-formation-earth-gi...

As for @CRR's argument about the Roche limit, that is nonsense. In the first place, his creationist source for the recession rate of 4.4 cm per year uses older estimates.

http://creation.com/the-moons-recession-and-age#en...

The recession is caused by tidal interaction between the earth and the moon, and the most recent estimates place the recession rate at about 3.78 cm per year, or about 1.5 inches.

http://www.bbc.com/news/science-environment-123111...

At a recession rate of 1.5 inches, that would be 106,534 miles over a period of 4.5 billion years (the age of the earth). The moon is on average about 240,000 miles away, which means that 4.5 billion years ago the moon would have been about 133,465 miles away. So how does that prove the earth can be no more than 1.37 billion years old?

A clarification is needed concerning that conclusion. Because the moon would have been closer to the earth billions of years ago, the tides would have been higher, thus increasing the interaction effect for each tide. However, because the moon was closer to the earth then, it would have had a greater orbital speed and a smaller orbit, which would have resulted in far fewer tides over the space of each year. The net effect of the fewer tides would have essentially cancelled out the increased tidal effect of each tide, so the rate of the moon's recession would not have been much different from what it is now.

Furthermore, there are currently two major continental masses that the tides impinge on to brake the earths rotation: the combined continents of Africa and Eurasia, and the combined continents of North and South America. However, in the distant past, there was only one super-continent, Pangea, that existed for a very long time. So with only one continental mass for the tides to impinge on, there would have been less overall tidal friction, and hence less energy transfer to the moon.

In any case, if the moon had been so close to the earth that the time of the moon's orbit around the earth would have been close to the time of the earth's rotation, it would have resulted in tides occurring only once every million years or so.

And if the moon had been even closer, the moon's orbit would have been geosynchronous with the earths rotation, which would result in the moon appearing to remain stationary over one spot above the earth. At that point there would have been no moving tides at all and hence no energy transfer and no recession.

The Roche limit of the Earth/Moon system is about 12,000 miles, much less than the geosynchronous orbit of 20,000 miles.

The moon is currently receding from the earth at about 4.4 ± 0.6 cm/yr. Calculations show that about 1.4 billion years ago the moon would have been at the Roche Limit. The moon could not have formed from gravitational attraction within the Roche Limit so this is the upper limit for the formation of the moon. This is about 1/3 of the estimated age of the earth.

The capture theory was popular until the 1980s. But most scientists have subsequently rejected it. Because the Moon's oxygen isotopic ratios seem to be essentially identical to Earth's. Which indicates that the Moon is largely made out of material that used to be on Earth.

The evidence is that the earth is filled with life. The moon's gravitational influence was party responsible for the conditions that allow life to flourish.

It does sound like a pretty good basis for a story. Talk about a world changer.

Proof...I'd say maybe... historical evidence of changing tides? Or some other measureable distortion of gravity that could be measured and traced back in time? hmm good one...

Since the earth and the moon were both once the same body this seems rather unlikely, don't you think?

Evidence of tidal effects present before that time debunk the theory.