Great post and thank you for the/your effort.Proof nobody can give, for any reasonably complex natural system. All one can do is critique the structure of an argument and pile up evidences.
If you are interested in why this is so, I suggest you read the classic To Save the Phenomenon by Pierre Duhem (a convinced Catholic, BTW, so it isn't atheist propaganda). You are waiting because reality is complicated, and proving anything by means of reasoned argument alone is like nailing jelly to a tree. That being said, what an atheist can do is identify the assumptions made, and identify how the evidence for and against an argument relates to the argument itself.
I think you will find that, if dispassionately examined, the (rational) evidence for the existence of a deity rests on the fact that the arguments for it are intuitively plausible, and the believer wants and sometimes rationally needs them confirmed. OTOH the atheist looks at such intuitions with suspicion, and often finds them mere prejudice, with only flimsy backing, often with contradictory evidence, and a position of doubt more plausible than conviction. The adumbration of deep skepticism around each argument rationally leads to agnosticism, and if consideration and personal valuation of rationality are favourable, atheism.
To give an example, the idea that every event is caused. Why must this be so? Intuitively, it seems obvious. Analytically, it is not at all: cause and effect seem ideas reflecting mere prejudice, albeit tempting, and the farther one chases the ideas of cause and effect, the more abstract, rarefied and frankly irrelevant the subject becomes. With an increase in certainty as to the irrelevancy of abstractions justified almost wholly by intuition comes the notion that very little is certain on empirical grounds alone, and thus metaphysical abstractions arising predominantly from intuitions about nature should be relentlessly simplified, insofar as possible, and always carefully and rigorously examined, as being poor guides to truth.
However, faith is still justifiable, IMHO, although not from a purely dispassionate view (again, IMHO) . The arguments I have sketched rely on intuition and plausibility to evaluate, as well as logic and evidence. Doubt has two faces: inclining towards non-belief, or inclining towards the possibility of a truth that may not be proven. It is a moral responsibility to pick which attitudes, evidences and justifications lead one towards a functional and healthy life, while respecting the latitudes that one's degrees of conviction for or against provide you. The first duty towards yourself is your own health, well being, and sense of truth and rightness (note: not righteousness, but rightness: again, my opinion). This leads people various places, that are not always compatible with each other, and the main challenge in my opinion is not actually to establish objective truth, but to live with one another. Others may be worried more about eternal torment or reward, but I can't do anything about that.
I would also add that sometimes experiential pheniomena are so deeply convincing of one argument or another that the person who has the experience literally has no choice but to be convinced of one side or the other. This is not uncommon and not to be sneered at. However, such phenomena work both ways: some people go through religious experience and emerge convinced that they have seen the deity, face to face. Others go through nightmare and emerge convinced that there is no possibility of such a being at all. Both are non-rational convictions, both are justified, and both I'd consider myself a fool if I argued with the individuals concerned about the conclusions alone.
How long are we all going to have world at war, and at war endlessly.. ? That is not Gods Will and God has allowed us, of course free will.. Israel of old was/is shown to us as a selective group of people who were always backsliding and who were always being punished by God yet to no avail ? Here is the issue with God..
Isa 46:8 Remember this, and stand firm. Keep it in mind, you rebels. 9 “Remember things that happened at the beginning, long ago —
that I am God, and there is no other;
I am God, and there is none like me.
10 At the beginning I announce the end,
proclaim in advance things not yet done;
and I say that my plan will hold,
I will do everything I please to do.
11 I call a bird of prey from the east,
the man I intended, from a distant country.
I have spoken and will bring it about;
I have made a plan, and I will fulfill it.
12 Listen to me, you stubborn people,
so far from righteousness:
13 I am bringing my justice nearer,
it is not far away;
my salvation will not be delayed,
I will place my salvation in Tziyon
for Isra’el my glory.