As pointed out in this question, there is no hard scientific evidence of the existence of an existentially all-powerful being.
As there is no direct evidence that there is a God, there is also no direct evidence supporting the theory that there isn't a God. How does modern science DISPROVE God (at least the concept of an all-powerful being who created the universe)?
Short answer: Depending on your definition of God, science either can't disprove God or disproved God long ago.
Long Answer:
If God is defined as a being who created the universe, then God can't be disproved as God can always remain beyond detection.
However, if God is said to have left certain marks that we can see, marks that uniquely trace back to God, then science may be able to find evidence for or against this God's existence. As a result, modern evolutionary theory challenges the conception of God that created people ex nihilo (or out of dust), and modern brain science challenges the role of God as moral arbiter and so on.
There's some philosophical import to this. This same concept -- that a being otherwise unobservable could be known by traces -- can be seen as a motivation behind theodicy. That is, if there is an omnipotent, omnipresent, omnibenevolent being, then this being should leave a mark on the world -- namely, a lack of suffering. Yet, suffering exists.
Further, what does a lack of evidence mean? What if we postulate the existence of (to use Bertrand Russell's example) an invisible teapot? Would we take the idea of this teapot with the same seriousness as we do of God? Why keep an open mind about God and not the teapot? Are we perhaps revealing a bias towards God?
Then of course scientists have personal beliefs, and some believe in God and some don't. While the personal beliefs of scientists should not matter, some scientists may issue proclamations, perhaps as a result of over-enthusiasm for the methods and power of science or what certain findings imply.
It doesn't
Science does not prove nor disprove God. Never has, and almost certainly never will. The idea that science disproves God is an unpopular attitude held by a few people who don't actually understand what science is, or how it works.
Those that claim science disproves God usually start from a scientifically valid claim that "there is no evidence for God." They then apply Occam's razor to simplify this to "the most natural reason for there being no evidence of God is that God does not exist." However, the application of Occam's razor is not scientific. It is a tool which is wielded by scientists from time to time in the process of doing science, but the final scientific product does not rely on it.
This is not to say that the application of Occam's razor here is not wrong, just that it isn't part of science. It's just a view that is well aligned with the results analyzed by science.
The desire to claim science disproves God is usually caused by one of two situations:
Other than those situations, most of the time individuals seem to be content with a "live and let live" sort of attitude, because in most situations the models of science are reasonably manageable within a religious setting, and vice versa.
My response to any such situation is to explain "science has not observed any data to prove nor disprove God. However, science has produced models of what the universe could look like which do not rely on metaphysical intervention. These models have a curiously good track record of explaining things we see in our lives. They do not claim to be perfect, but they have been sufficiently helpful that virtually all of humanity now embraces at least portions of their results."
In most cases I have found, those who claim science proves or disproves God's existence lack an understanding of science's fundamental roots in statistics. This is particularly true in the evolution argument. I consider this mostly the responsibility of the atheists who have made the mistake of arguing "the theory of evolution is true," which misrepresents its statistical basis. There is a monumental difference between a confidence of 99.99999% and a confidence of 100%>
The alignment of a scientific worldview and atheism often come back to the ideas embodied in Russel's teapot or Sagan's Dragon
if the god under consideration has observable effects, we have not seen them,
if it doesn't have observable effects, then why propose it in the first place? (or what does it mean to say it exists?)
Note that these lines of reasoning are primarily about how the existence of God does (or does not) relate to empirical observations about the world -- if anything, science involves using/interpreting empirical observations. These considerations address the "know" question in the title.
This line of thinking doesn't DISPROVE god(s) in a logical sense, but provide a way for some people to align aspects of the scientific method with atheism. In addition, it is not required that one take a scientific approach on the existence of gods, e.g. some people think that the tri-omni god is logically inconstent, and thus have a logical (not scientific) basis for claiming "no tri-omni gods exist".
How does modern science DISPROVE God (at least the concept of an all-powerful being who created the universe)?
I would go as far as to say that once one begins talking about the attributes of God, they are no longer doing Science, they are doing Philosophy.
Science isn't in the business of proving/disproving anything, the scientific method is one where we analyse competing hypotheses and confirm/disconfirm them based on evidence.
Proof is a logical and mathematical concept, not a scientific one.
The idea that Science can "disprove" God hinges on the notion that God is a scientific hypothesis. Unless you're a fan of Richard Dawkins-esque incursions on Philosophy, you won't find the aforementioned to be particularly compelling. Ask any theist to define their God, surely one term that will almost always come is "nonphysical".
One could maybe run a sort of evidential argument against theism, given the history of science... but this does not prove that there isn't a God.
Overall, I'd say that Science can help us cast doubt upon certain God models (physical ones mainly). Nonetheless, I am of the belief that Science on its own, isn't the best approach with regards to analysing the God of classical theism.
The biggest issue with "God" is defining what this means. You can always point to everything (or just something) and say that it is "God". Then you have proved that "God" does in fact exist. On the other hand, what would it take to prove that a more literal (and literary) God does exist? A seemingly all-powerful being who came down from the heavens and starting moving mountains would be pretty quickly labeled an advanced extraterrestrial by most scientists. It would certainly not be possible to disprove the "extraterrestrial hypothesis" if such a being showed itself.
Why are you expecting the study of the natural world to tell you anything about that which may or may not transcend it? This is not a question that science even aims to answer. Maybe you should look at a more suitable area of study that may be better equipped to answer this question.
If I can demonstrate your faulty logic let me just ask you what scientific evidence is there that Germany invaded Poland in 1939? None? So that means Germany did not invade Poland in 1939?
One thing that brought me to atheism, a long time ago was the idea that the universe arose spontaneously; when I read it - as a quantum fluctuation, but its also in Aristotle:
But chance also and spontaneity are reckoned among causes: many things are said both to be and to come to be as a result of chance and spontaneity.
There are some too who ascribe this heavenly sphere and all the worlds to spontaneity. They say that the vortex arose spontaneously, i.e. the motion that separated and arranged in its present order all that exists.
But this, when you think about it involves an infinite regress of cause; this is particularly clear in the Quantum Fluctuation notion; since it requires the laws of QM to 'exist' whatever this means; but it certainly means something since there is a certain technique in physics to modify the laws that we know to see what could be otherwise, and also to find out more about what we do know.
He adds:
Others there are who, indeed, believe that chance is a cause, but that it is inscrutable to human intelligence, as being a divine thing and full of mystery.
