From the Carrier-Wanchick debate, which I am linking to .
Carrier's Atheistic Cosmological Argument from his Debate with Wanchick.
Atheistic Cosmological Argument (ACA)
The universe is almost entirely lethal to life. By far, most of existence is a radiation-filled vacuum, and there are easily a trillion times more dead worlds than life-bearing planets. Life is clearly an extremely rare and unusual product of the universe. We also know it took the universe billions of years to finally produce any life anywhere, and then only an extremely simple single-celled life form. Then it took billions more years of a long, meandering and often catastrophically failing process of evolutionary trial-and-error to finally produce human beings. CN explains this state of affairs better than BT, since this state of affairs is highly probable on CN but not particularly probable on BT.
Even if a God might have some reason to build a universe this way, he had many other ways he could have chosen (like the way the Bible literally depicts and early Christians believed), and some make more sense on BT (a God has no need of a universe so old or big, for example). But we know of only one way CN could produce human beings: pretty much the way they were, with vast ages of unguided trial-and-error spanning across vast stretches of life-killing space. For example, if CN, then (a) life could only be an accidental byproduct of the organization of the universe, but (b) the only way life could then exist is if the universe were so incredibly old and big that something as improbable as the origin of life would be possible, yet (c) that is exactly the universe we find ourselves in. We have no comparably good explanation for why the universe would be so old and big on BT, or for many other peculiar features of our universe. Therefore, CN is a good explanation for why we observe what we do, while BT is not.
P21: If CN is true, the nature and scale of the universe, and the history of life that we actually observe, is the only possible way we could exist that we know of, and is therefore what we would expect to observe.
P22: If BT is true, the nature and scale of the universe, and the history of life that we actually observe, is one of countless possible ways we could exist that we know of, including some that make more sense, and is therefore not what we would expect.
C10: Therefore, per logicum, CN explains what we observe better than BT.
1. I crossed the street today.
2. If naturalism is true, then the only way I can do that is by walking.
3. If God exists, then there are many ways I can get across the street besides walking, because, for example, God could cause me to apparate across the street Harry Potter style.
4. Therefore, we have evidence that God does not exist, based on the fact that I walked across the street today.