Ah, yes, that age-old question argued between seculars and non-seculars, Atheists and Christians, and greatest minds of our times. We've had the debates here before, numerous times, and it's always interesting to me, how we never begin by setting some foundations of understanding with regard to context. We immediately seem to jump into the usual talking points, and have the same argument over and over. Let us attempt to slow this down a bit, and begin by coming to understanding on the meanings and context of the question, before we attempt to answer the question.
We need to agree on what 'exists' means first. Do we mean, in a physical sense? I think it's safe to say, God doesn't exist in a physical sense. Most forms of belief in a god, require the god to be superior to physical man, therefore, we can presume any God would have to exist in a form outside of our physical world. Can we agree? Now, I can say that I know the Christian religion, for instance, believed God existed in a physical man, Jesus Christ. Much of their religious doctrine of belief is centered around his teachings, but for the most part, God's are not of the physical world, they are superior beings or entities, and outside of our physical universe. Given this information, to require God to exist in a physical sense, or to be proven to exist by physical sciences, is pretty useless and irrelevant.
So, God doesn't exist in a physical sense, and it's pointless to try and prove existence with physical parameters. In order to properly examine the question, we need to evaluate 'exist' as meaning, in a spiritual sense, because that is what God is, a spiritual entity. Now, whether something 'exists' in a spiritual sense, is very difficult, in fact, impossible to prove or disprove. Much of this relies on faith or comprehension of the individual. For instance, let's take something else that is 'not of the physical world' like a dream, and examine this. When you have a dream, did the events actually happen in the physical world? No, of course not. But the events did happen in your dream, you remember them vividly. You can come to me and tell me what you dreamed, and I can choose to have faith and believe you, or not. You can't physically prove you dreamed what you said, and your dream is in essence, your comprehension of what you recall. Did the events of your dream take place in the physical world? Then why would you require physical proof of their existence? To properly evaluate a spiritual entity, you have to apply spiritual criteria, which largely relies on faith.
Now, you will say, but we need more than "faith!" And the simple fact of the matter is, even the most sophisticated math and science, relies on faith. The very principles of all physical science, rely on the order of the universe to remain the same at all times and never change. Gravity always works in a predictable way, we have faith that it will continue to do so. If you believe in a theory of evolution, you must have faith the theory is correct. So we have faith in whatever we believe, whether it is faith in physical science applied to the physical universe, or spiritual faith applied to the spiritual realm. To conflate the difference between physical and spiritual realms, is often the result on not first properly defining the context of the question. If we are going to honestly ask the question, we must apply the proper parameters and context. We can't leap back and forth from the physical realm and demanding physical proof, and back to the spiritual realm, they are two different things.
It would be as if, you have someone who doesn't believe in physical sciences and thinks the rain is caused by God crying. You can show him all the physical proof you want, but he doesn't believe in the physical sciences. He refuses to acknowledge them, and insists the rain is caused by God crying. You ask him for 'proof' and he promptly replies; "Because God told me so! Can you prove he didn't?" Of course, you can't, and he is basing his belief on a spiritual faith, devoid of any belief in physical science, but the point is, rain is not caused by God crying, we know through physical science, what causes rain. The same can be said for seculars and Atheists, who demand physical proof and refuse to acknowledge the spiritual realm. If you aren't willing to open your mind to the possibility of something else, you will remain as ignorant as the example presented, closed-minded to understanding and in the dark on this most prolific question.
The spiritual evidence for the spiritual existence for a spiritual God, is overwhelming. Countless spiritual believers can attest to this. Accounts of people overcoming tremendous adversities, outright 'miracles' brought about through their faith and prayers, years of oppression and bondage overcome, great nations created. The evidence of God's work can be seen in our flowers and life, in our mountains and sunsets, and in the face of every newborn child. Tracking our civilizations, we find that mankind has always been spiritual in nature. Psychologists have said, if God didn't exist, man would have to invent it. We are hard-wired this way, to worship in a spiritual way, something greater than self. This has been an aspect of humans since humans began. Some believe, it is ultimately what led to the rise of modern civilization.
Now, being that humans have always held this particular character trait, and we know through studies of animal behavior, all inherent intrinsic behavior is present for a reason, we have to presume there is a reason for humans to be inclined to spirituality, there is no other scientific explanation for this. To this day, 95% of the world population, believe in something greater than self. Of course, these beliefs range widely, and to varying degrees, but only 5% are true Nihilists, and do not believe in anything at all. We can't argue with the physical sciences here, if the species has always worshiped, there must be a fundamental purpose for it. So sayeth, Darwin, anyway.
The bottom line is, we haven't really answered the question, because the question is subject to interpretation and understanding of context. Regardless of which way you answer the question, your answer relies solely on faith and you have no physical evidence to support it. However, the spiritual existence of God doesn't require or need physical proof.
