Man is not the measure of God. When he tries to be, it is he that is irrational.
The most beautiful and deepest experience a man can have is the sense of the mysterious. It is the underlying principle of religion as well as all serious endeavour in art and science. He who never had this experience seems to me, if not dead, then at least blind. To sense that behind anything that can be experienced there is a something that our mind cannot grasp and whose beauty and sublimity reaches us only indirectly and as a feeble reflection, this is religiousness. In this sense I am religious. To me it suffices to wonder at these secrets and to attempt humbly to grasp with my mind a mere image of the lofty structure of all that there is. - Albert Einstein, “My Credo,” presented to the German League of Human Rights, Berlin, autumn 1932, in Einstein: A Life in Science, Michael White and John Gribbin, ed., London: Simon & Schuster, 1993, page 262.
God cannot be put under a microscope or observed with a telescope. God created space, time, energy, matter, physical laws, logic, reason. He is not described by to limited to the things He created.
A rational man, realizing that all of these things would apply in his quest to "prove" God, would instantly lay down his naturalist toolkit of sensory perception and reason and fall to his knees in prayer asking God if He exists, please reveal Himself.
One of the ancient manuscripts in Charlesworth's Pseudepigrapha tells a backstory to Genesis 12 - the calling of Abraham.
In a nutshell, the story goes that Abraham's father was idol maker. And one day, one of his carved idols fell into the fire and burned up. Abraham was aghast thinking how could this be a "god" when it is consumed by fire.
His dad wasn't moved. He said that was the way the "god" gave him warmth and allowed him to prepare his meat. But Abraham, as the story goes, fell to his knees and asked God in prayer, if you really exist please reveal yourself to me.
Moreover, when a man deliberately denies God, God gives him over to a reprobate mind.
And even as they did not like to retain God in [their] knowledge, God gave them over to a reprobate mind, to do those things which are not convenient; - Romans 1:28
The reprobate mind has no understanding, no moral ground, it hates God and the things of God. It is blinded and deformed, no longer capable of logic or reason.
Being filled with all unrighteousness, fornication, wickedness, covetousness, maliciousness; full of envy, murder, debate, deceit, malignity; whisperers, Backbiters, haters of God, despiteful, proud, boasters, inventors of evil things, disobedient to parents, Without understanding, covenantbreakers, without natural affection, implacable, unmerciful: Who knowing the judgment of God, that they which commit such things are worthy of death, not only do the same, but have pleasure in them that do them. - Romans 1:29-32
God's Name is I AM.