The one that you will find more believable between Genesis and the Big Bang Theory depends upon your philosophical starting assumptions. If you look at the evidence from a theistic creation perspective, you will find Genesis to be the most believable. If on the other hand you look at the evidence from an atheistic, naturalistic materialistic perspective, then you will be forced to accept the basic Big Bang to man story regardless of what the evidence actually is.
If you start with the atheistic naturalistic materialistic philosophical presuppositions behind the Big Bang which started from a singularity and expanded outward eventually forming stars, galaxies life, and intelligent life that to evolved without guidance or purpose into human beings. You are forced to ignore the fact that all of our research indicates that naturalistic abiogenesis is thermodynamically impossible, and that it is so improbable that it would probably requires many more orders of magnitude more events than there are possible events in the Big Bang model of the universe to have possibly of any chance of coming up with a functioning cell. If because of these atheistic naturalistic materialistic philosophical presuppositions, you throw out any possibility of an intelligent designer behind life despite the abundance of evidence you will consider the Big Bang model to be more believable because there is no other alternative regardless of what the evidence and no laws of physics may actually say.
If, however, you start with the historically recorded account reported to have been provided for us by the creator himself then you have none of the thermodynamic or other difficulties associated with the Big Bang Theory or developing living systems because you have an intelligent designer to handle them. Furthermore, you are free to include the possibility that we could be in a privileged place in the universe because we were created by the God who created everything around us, this solves a lot of the problems in cosmology that exist because of insisting on the cosmological principle. In this case, you would find the Genesis account to be the more believable account of origins.
What happened in the past, which one we find more believable, is going to depend upon our starting assumptions. If those starting assumptions exclude God before you look at any of the data, then it will be impossible for you to find the Genesis account to be believable regardless of the evidence.
References:
https://www.timesexaminer.com/charles-creager-jr/11687-abiogenesis-a-thermodynamic-impossibility
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