There is no direct scientific evidence for the existence of God. However, this does not tell us anything about God. It only tells us something about science.
To see why this is so, we must first understand what science is. In essence, science is a process with four steps: 1. Systematic observation of the physical universe. 2. Discovery of regularities in the observations. 3. Proposal of explanations for the regularities. 4. Testing the explanations to see if they actually describe the real world.
The "explanations" in steps 3 and 4 are either newly-proposed natural laws or, more frequently, new applications of already-accepted natural laws.
For the sake of argument, assume that God exists, even if you don't believe it. And since the word "God" means different things to different people, let me define what I mean. By "God", I mean a being who exists completely independently of the physical universe; He stands "outside" it, outside even the relativistic fabric of space-time. He created the physical universe. And He can, at will, reach in to the physical universe and alter any aspect of it that He chooses. (Computer people may think of this as similar to using a debugger to modify a running program. From the program's point of view, a variable or instruction changes "out of nowhere" - with no cause from within the normal execution of the program.) When God changes something in the physical universe, it really changes. It's not just a change in the mind or attitude of someone; it's a real physical change. That is, it's a change that science can observe. All this I ask you to assume for the moment.
Now, the question is, if science observed the effects of God intervening in the physical universe, what would science do with it?
The first thing that science would do is throw away the observation, at step 2, because it was not repeatable. There would be no regularity to observe; it would be a one-time event. No scientist could make it repeat, because no scientist could make God choose to do it again.
But if science did not throw away the event because it was non-repeatable, in step 3 it would propose an explanation. Recall that these explanations are by means of natural laws. That is, they are purely natural explanations for the observed effects. And if anyone were to suggest that God might have had a hand in things, their suggestion would be dismissed as "unscientific".
And even if such a suggestion was seriously made, the next problem comes at step 4. You simply cannot devise an experiment that will prove that God intervened in the physical universe.
Thus, there cannot be any direct scientific evidence for the existence of God. Science concerns itself with natural laws that govern natural events, and is blind to everything else.
At this point I need to say a few words in defense of science. If I am a scientist, I have to assume that what I observe is the normal working of the natural universe, rather than some kind of miracle. I have to assume this or I cannot do any science.
Also, science is full of things for which there was no scientific explanation - and then, eventually, someone figured it out, and then there was a scientific explanation. Scientists therefore have grounds for skepticism when told that "science cannot explain this."
But many scientists go a step further, and conclude that the natural, physical universe is all there is, and that natural laws can explain absolutely everything. This conclusion is not something that has been proved scientifically. It turns the methodology of science into a philosophy.
The net effect of both the scientific methodology and the philosophical viewpoint of many scientists is that science is blind to anything outside the natural universe. If there is anything more to reality than the physical, science - at least in its present form - will never find it.