The mutation rate necessary to explain the genetic differences between humans would have to be at least 20 times that which is actually observed in order to support the "theory" that the most recent common human ancestors lived 6,000 years ago. Of course, strictly speaking, this doesn't make it an impossibility. The gods could easily have manipulated the genomes of early man in order to make it appear that humanity is far older than 6,000 years. Similarly, they could have independently created chimpanzees with nearly identical DNA to humans - right down to the junk DNA in order to make it appear - for their own reasons - that humans and chimpanzees have a common ancestor. With this in mind, we might have to go to the evidence provided by other sciences. But then, the gods could just as easily have interfered with the half-lives of isotopes to make human artifacts appear older than 6,000 years, or created artificial fossils of hominids that never existed in order to make it appear that humans evolved from apelike ancestors. They could have - in the blink of an eye - laid down layers of ice in the Arctic to give a false history of our planet. They could have filled the planet with dinosaur bones and meteor craters and layers of different kinds of rock, with different kinds of fossils in each layer, all on some divine whim.
So you're right, hooberus. Your beliefs can never be conclusively proven false, unless we set aside the possibility of deceptive deities. Of course, once we do this, you will accuse us of having a naturalistic bias, of a priori dismissing the idea of divine intervention.
So there we have it. We can never ever know anything for sure. Evidence is unimportant because any omnipotent entities we care to postulate could have manipulated it for their own ends. So, hooberus, where do we go from here?
I hope to respond to the above pot when I get more available time.