Even the most pious believer has to admit that there is no scientific evidence for God or anything else supernatural. If there were, it would be in the textbooks along with the evidence for electricity, gravity, neutrinos, and DNA. This doesn't bother most believers because they have heard many times that "absence of evidence is not evidence of absence."
However, just repeating a statement over and over again does not make it true. I can think of many cases where absence of evidence provides robust evidence of absence. The key question is whether evidence should exist but does not. Elephants have never been seen roaming Yellowstone National Park. If they were, they would not have escaped notice. No matter how secretive, the presence of such huge animals would have been marked by ample physical signs -- droppings, crushed vegetation, bones of dead elephants. So we can safely conclude from the absence of evidence that elephants are absent from the park.
For thirty years physicists have been searching for a particle called the Higgs boson that hypothetically plays a key role in the universe, so important that it has been referred to (perhaps facetiously) as the "God Particle." In the standard model of particles and forces put in place in the 1970s and consistent with every observation since, Higgs bosons pervade the universe and generate mass, the very stuff of matter. We have failed to observe them so far because we have lacked the necessary instruments. However, there are good theoretical reasons to believe that the Large Hadron Collider (LHC) in Geneva, now accumulating its initial data, should provide evidence for the Higgs. If it does not -- a prospect most physicists regard as possible -- then the Higgs boson would be shown not to exist.
That is the situation with the Judeo-Christian-Islamic God. Until recent times, absence of evidence for his existence has not been sufficient to rule him out. However, we now have enough knowledge that we can identify many places where there should be evidence, but there is not. The absence of that evidence allows us to rule out the existence of this God beyond a reasonable doubt.
Now, I am not talking about all conceivable gods. Certainly the deist god who does not interfere in the world is difficult to rule out. However, the Judeo-Christian-Islamic God, whom I identify with an uppercase G, is believed to play such an active role in the universe that his actions should have been detected, thus confirming his existence. Let me present four examples.
I will begin with the origin of the visible universe. Our knowledge today allows us to push back in time to barely a trillionth of a second after the universe began. Extrapolating from there to the origin, we find that the universe began in a tiny (but not infinitesimal) region of space. Now, information only exists when it is embodied in some physical system, and we know that there is a limit to how compact information can be. This tiny region of space could not have contained more than a few bits of information -- far too little to specify the universe that evolved from it.
As the universe expanded, it could hold more information. This created an environment in which order could emerge -- as, over time, through an endless series of random events, it did. But the tiny amount of information contained in the very early universe was not enough to include any plans of some creator at that time. This allows for the possibility of a deist god who set things up, started things going randomly, and then left. It does not allow for some specific plan of creation to be embodied in the universe from the beginning. A God with such a plan can be ruled out beyond a reasonable doubt.
Next, consider the claim that the universe was designed. Many people give this as a reason to believe in God. They cannot see how the order of the universe can have come about naturally. However, observations in physics, cosmology, and biology have been scoured for evidence for design in the universe, evidence that should be there if there were a designer God. None has been found. This includes the frequently heard claim that the parameters of physics and cosmology exhibit a fine-tuning for the evolution of life. That subject will be covered in great detail in my next book: The Fallacy of Fine-Tuning: How the Universe is not Designed for Us. My conclusion is that the claims of fine-tuning are based on inadequate knowledge of physics.
Intelligent design in biology has been thoroughly refuted in recent years, so I need not say much. Everywhere biologists look they find evidence of randomness and haphazard arrangements that would be called incompetent if they were designed. No matter where scientists cast their eyes, the universe they see looks just like it should look if there was no divine design.
Third, consider the supposed power of intercessory prayer. Well-executed experiments by reputable institutions such as Harvard, Duke, and the Mayo Clinic have failed to find that prayer improves the recovery of hospital patients. Apologists simply say God did not choose to respond to this test. But you can bet they would have changed their tune if the results had been positive. Trillions of prayers have been tendered over millennia. Of course, most sick people get better anyway, except once. If the God most people worship and pray to does exist, intercessory prayer would have a better batting average than what you would get from the normal operation of the natural world, including luck. It doesn't.
As the final example, the Abrahamic God is believed by his worshipers to talk to people and provide information they otherwise did not know. Nothing could be easier to test scientifically. All you have to do is find a few examples where a truth has been revealed that later was confirmed. This could be something simple, such as a prediction of some future event that turned out to be confirmed. This has never happened.
Of course, claims of revelation can be found in all three monotheisms, but none stand up to critical scrutiny. The so-called prophecies in scriptures were all made in the distant past and can't be tested since the events prophesied have already happened, or, as in the case of Jesus returning in a generation, long been falsified.
In all of these examples, evidence for God should have been found, but was not. This absence of evidence is evidence of absence. It refutes the common assertion that science has nothing to say about God. In fact, science can say, beyond any reasonable doubt, that God -- the Judeo-Christian-Islamic God -- does not exist.