Like it or not, atheism is the default position. Theism is not automatic or inevitable. Theism is not natural. The gods all have to be learnt. They are new information superimposed over the default: a-theism. If this were not the case a single religion centred on a single deity (who we’d expect to speak a single language) would arise naturally and fluidly wherever humans were found, regardless of their isolation or epoch. That, of course, is not the reality. As much as Christians would like to believe otherwise no person has ever arrived at Christianity without it first being taught to them. Mithraism never suddenly appeared in Malaysia, or Mormonism in New Zealand. Without specific guidance no person has ever discovered Islam or Judaism like Newton discovered classical mechanics and gravitation. Scatter ten thousand people and give them ten thousand years to develop in seclusion and no two will arrive at the same superstitions or invent the same religion, but all ten thousand will, however, eventually stumble upon the theory of gravity. It is the theist therefore who is introducing a new element (their particular, geographically centric, linguistically and culturally specific god) to the natural canvas, and it is therefore the theist to whom the burden of proof falls.
A positive claim (unicorns exist) requires evidence. A negative claim (unicorns do not exist) requires a complete lack of evidence. As no evidence exists for unicorns the positive claim (unicorns exist) must be considered false until proven true. This is only rational. The negative is however easily falsifiable. All the unicorn believer needs is one solitary piece of reasonable (even inferable) evidence for the existence of unicorns to shift the entire burden of proof requirement onto the non-believer. Said in another way, any un-falsifiable claim (unicorns, spacefaring turtles, gods) must be read as false before being proven true. It follows then that there is no need for atheism to prove the non-existence of the gods, nor indeed for naturalism to prove the non-existence of the supernatural. Unicorns, spacefaring turtles and gods are not natural, they are the aberration, and should a theist wish to be accepted as a rational human being then it falls to them to present the evidence needed to substantiate the claim. Until such allegations can be supported all positive claims must be considered deviant and abnormal.