Except by pure reason, as Einstein reasoned it.
First of all, Einstein, although a spiritual person in many ways, was still an atheist. Secondly, he never operated by "pure reason." He operated by intuition via mathematics.
However, I will agree to this extent: asking for a scientific proof of God is nonsensical. God is not a statement of fact about the observable world; he is therefore outside the purview of science. But by the same token, we do not and should not include God as a hypothesis within scientific models.
The genetic and fossil evidence that we have cannot explain away the implausibility of the intricate, beautiful symmetry and asymmetry and incredible diversity that has come out of presumed chaos or how the stuff of the universe came to be in the first place or how it was able to organize itself into the chaos leading to the big bang.
First, "how the stuff of the universe came to be in the first place" is not a scientific question, and therefore the failure of science to answer it is not an appropriate criticism. Secondly, however much you may FEEL that the "intricate, beautiful symmetry and incredible diversity" of life or of the cosmos defies explanation by evolution, that is not in fact the case. Given the
existence of living organisms (again, don't confuse evolution with abiogenesis or the study of life's origins; that's a different branch of biology), evolution suffices to account for what we see in terms of speciation and the development of biological complexity.
You must remember that we are dealing with very long time scales here. What may seem highly improbable on first glance can become very high-probability indeed given a sequence of many trials for each step over many millions of years.
To assume that all that happened without benefit of some sort of intelligent design--I'm not saying that has to be God as Christians or Jews understand God because Einstein certainly didn't understand it that way--but to assume all that happened by accident requires far more faith than believing that some sort of intelligent design was behind it.
I disagree, and I say that as a spiritual person. But God, whatever he/she/it may ultimately be, is not something that can be found through objective evidence from observation of the world around us. God is found in another way altogether, having nothing to do with science.
God is found through direct personal experience of oneness with all-that-is, by listening to the still small voice within, by opening the heart to wonder. That is what faith really is all about. There is no conflict between God and anything in science -- including evolution. But nor can we assert that science should or must include God as a hypothesis, saying that the universe must have been designed by intelligence. We have no objective evidence that this is so.
Science can be as much logic and reason re what we cannot test or falsify as it is based on what we can test or falsify. Some of the greatest scientific minds in the known universe--Einstein being one--understood that
Again, you are misunderstanding or misrepresenting Einstein. Every statement Einstein ever made as a scientist was falsifiable. Do not confuse the technical inability at the moment to conduct an experiment with true non-falsifiability, which requires a logical inability to perform an experiment with any technical equipment ever possible to be devised.