Life without God is going to be existence without experiencing anything that could be considered good. There is no other possibility. No sunshine, no waterfalls, no baskets of puppies, no fulfilling relationships, no love. God is the author of good. If we reject God (the real one as opposed to the one we sometimes imagine) we are rejecting ALL that is good.
There are places on the Earth where the neither the Bible or Christianity has ever been heard of. Everyday, for generations upon generations, the people live happy lives and experience both "good" and "bad". People are born, live, and die never knowing of the God of the Bible. It doesn't phase them one bit.
There is a saying in India - "The only atheists are the people who attended Catholic school."
people sin because they have a sin nature. It is our nature to sin, so we do. We do not naturally want God as our father. We want the object of our devotion to be an idol, religion or an organization. We want one that is performance based so we can a least take a little bit of credit for our good fortunes.
People "sin" because they have desires and wants that are harmful. Greed, aversion, and ignorance are the roots of these desires and therefor are the roots of suffering. This is not necessarily inherent in us and we can extinguish these desires on our own through practice. Therefor we can choose not to have a sinful nature. Adam and Eve were created without a sinful nature and still chose to sin.
The Law of Cause and Effect also establishes that our actions determine the response of the universe. Refrain from what is bad. Do what is good. Act in such a way as to benefit all beings. Do this and receive this. We make our own heaven and hell. The suffering we experience is made by us and therefor only we can save ourselves. There is also no need for anyone else to punish us. We punish ourselves.
why would anyone seek to live eternally in the absence of anything that could be considered good?
"Eternal" by definition means to have no beginning or end. So, if I am an eternal "soul" inhabiting a body where did my soul reside prior to my conception? Does this also mean that I was never created as eternal means no beginning or end?