None. What evidence can you put forth of an eternal creator?what evidence can you put forth of an eternal existence of this universe?
The way I see it, the universe indisputably exists and has existed for a very long time. We don't yet have the physics to extrapolate back beyond a certain time, but there are a number of ideas for how it could be either eternal or temporally finite but unbounded, that are not inconsistent with the physics we do have.
OTOH, we have thousands of origin myths & legends, and thousands of descriptions of gods, some of which are creator gods, many of which are contradictory (i.e. cannot easily be explained as different interpretations of the same thing), and all of which have the hallmarks of human imagination and story-telling. The claims made about them are unsubstantiated or untestable and we have no evidence that any of them exist.
So both science and origin myths & deities attempt to provide satisfying explanations for the unexplained history or origin of our universe.
Science has a proven track record of describing and explaining the universe, so I'm prepared to wait and see whether we can discover any more about the history and/or origin of our universe.
The explanatory power of origin myths and deities appears limited to their influence on human behaviour, so I see no reason to give significant credence to any of them, whether they happen to be currently popular or not.
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