There was a time when Earth had no Moon. About 4.5 billion years ago, when our ancient Solar System was still forming, the dark night sky above our primordial planet was moonless. At this time, the Earth was about 60 percent formed, although it did have a differentiated crust, mantle, and core. This was a very chaotic and violent era in our Solar System's past, with planets first forming out of blobs of primordial dust, gas, and rock. During this era, frequently likened to a "cosmic shooting gallery", collisions between the still-forming planets were commonplace. Orbits were not as orderly as they are now.
The very productive Cassini mission might attain some indirect information by analyzing the ring arc material--however, it is unlikely to come close to the little moon again before the mission ends in 2017.
Why hide these accomplishments? It has been difficult to argue for a conspiracy because no theory has offered a sufficiently convincing motive. An idea called "the frontier theory of history" provides two.