This is interesting, because I have come to realise (over many years, decades in fact) that the reality of God is in a sense prove-able; but that there is no specific proof - or at least no generally applicable, and generally effectual specific proof.
And I think I see why this is the case. People who think about the ultimate nature of reality ('philosophers') and try to explain anything; will find that this cannot be done without assuming an underlying coherence and also assuming that it is possible for us (individual specific 'me') to understand such things.
Yet, any specific proof will also require assumptions, which the doubter can recognise as such. And any 'proof' brief and simple enough to be effective, will - to that extent (brevity and simplicity) - be an obvious 'model' of reality (not actual reality itself); hence obviously incomplete and distorted in its representation of reality.
So, no proof really can stand alone as a proof, because no proof (because it is a highly simplified model) is necessarily applicable to reality.
Furthermore, all these aspects of proofs exacerbate the impression of circularity. In a sense, logic is always tautology - it is merely (at best) a clarification; a re-expression of one proposition in terms of another which means the same. Therefore, the 'answer' is already built-into the question - and the truth of any proof depends on the truth of what goes-into it...
All the above are reasons why, to an atheist, proofs of the reality of God seem always faulty, and seldom or never convince.
Yet, in a very broad and philosophical sense, I think there is a solid consensus across the ages among people who think about the ultimate nature of reality, and who keep thinking - who don't stop short - that this is a purposively-created-universe. And in this kind of sense God is certainly real (although what kind of God, and the nature of the purpose, are subject to great disagreement).
Why doesn't everybody converge on this? Why, instead, for the past few hundred years, have so many people decided that the universe of reality is incoherent; some meaningless, contingent combination of determinism and accidents?
The main reason is probably that - once adopted - an assumption of meaninglessness, incoherence, purposelessness... cannot be refuted. What can be refuted is the assumption that incoherence can be proven true by argument - yet this is perhaps the commonest modern belief; some version of the idea that 'science has proved' that reality is incoherent...
How then, starting from the typical starting place of assumed-incoherence, can modern man grasp the necessity of creation, of God?
I think the answer is perfectly simple; but I also recognise that a situation of perfect simplicity is one of the most difficult for anybody to attain. It is to go deeper and deeper, introspectively, challenging each assumption, pushing back from surface assumptions to what lies below; until one reaches a base which is solidly-assumed.
Different people will reach this base in different places - but all those places are interlinked, and derive from the same core. For some, it will be a core moral certainty; for another it will be that truth is real and a-good-thing; for someone else it will be their love for a person; for rare individuals it may be a rock-solid knowledge of beauty in music, landscape, poetry...
None of these (nor all of them together) amount to a 'logical proof' of God - but then that is not being sought. One is not trying to convince somebody else, but oneself. It does not matter if nobody else in the world would be convinced.
Love of a specific parent, spouse, child - for instance (or the beauty of a particular poem, or the vital nature of a special truth in science) may be unique to an individual. The point is that - for that person - this-thing-is-real.
It is real-er than anything which might be supposed to deny or refute it (such as 'what other people say' or any kind of 'evidence'... which may or may not be correct, may be misunderstood. (other people may lie, be incompetent - or be deluded.) It feels realer than anything which supposedly contradicts it; and when poked at from any angle, it stays solid.
Furthermore, things must be known at a level of simplicity that rules-out misunderstanding. They must be grasped-whole. So our knowledge of the reality of God or creation needs to be as a plain fact. We need to know God/ creation is real, not know somethings 'about' God/ creation.
The coherence of reality of God, that reality was created... such (linked) things must be known in this kind of way; that is, more solidly experienced than anything which might challenge it.
In this sense the reality of God can be proved: sometimes proved to our-selves, but never to others; proved as a simple fact that I personally grasp whole and without words, but never proved as a linguistic unit - sentence or paragraph - because that will always be an inexact representation of the primary experience, may be ambiguously expressed and wrongly understood.
If we set-out to seek proof for our-selves, and are serious about it, and stick at it (mentally, as a philosopher must); then the single, simple truth of God can be reached from many directions; and known solidly.
