The oldest rocks found so far on earth are between 3.8 and 3.9 billion years old. In minerals inside some of those rocks are about 4.1 to 4.2 billion years old. The earth must be at least as old as any formation on it.
Neanderthals were one of the more advanced populations of pre-historic humans, there are Homo habilis and Homo erectus which occured even before them are were most certainly not humans.
That seems a whole lot more likely then God creating a man out of nothing, then taking his rib and making...