I spend far too much time ruminating on theological concerns. It has been pointed out that this could be a form of OCD- obsessive compulsive disorder. Certainly its not fruitful, and I find years go by and I go around and around in circles philosophically. So where is my 'mode, median, and mean' belief system? I consider it to be a subset of the perennial philosophy though my spiritual practice melds hermetic, druidic and Christian themes....
God is, I have no idea how to prove that. God is unknowable in essence for that essence is transcendent. I have arrived at a consistent point of definitely not believing that God and the Cosmos are identical you might say, why retaining the insight that the divine is present 'in some powerful sense' within and through creation - creation manifests the divine will and power.
To resolve the question of divine transcendence versus immanence, I have rather seized upon and somewhat reinterpreted the idea that there divine 'energies' flowing from deity which are distinct from the absolute divine nature - to borrow a notion from Orthodox Christianity - and these energies are penetrating all creation and sustaining it.. The best metaphor for this, I think, is of the distinction between the Sun itself and the divine rays of light-heat that maintain life on earth. Clearly the sun is not on earth in the absolute says, but 'is' in a relative, conditional sense: we only experience the sun 'through' an experience of the light/heat never directly (to stretch the metaphor further, I'd also point out that no one on earth can look at the sun for very long). When we - pagans in particular - find creation, the cosmos to be 'divine', this is because we are seeing these 'energies' in action of fourfold providence: forming, animating, harmonising, preserving. I rather think 'nature' in all its plurality and variety represents different 'modes' or 'modulations' of this divine energy, and personified these modes or modulations of divine energy are our 'gods' or 'daemons' providing being, life and consciousness to the various aspects of nature.
The biggest challenge to belief in God is gratuitous evil. I certainly don't believe all evil has got a particular purpose, or is 'for the best' for particular individuals. I do though find it difficult to imagine a world that does or could not contain evil, because a physical world is necessarily limited and finite, also such a world can only be sustained in operation by hard laws of cause and effect that may cause havoc and destruction to individuals.
I have no doubt that a physical world like ours cannot be 'perfected' to be without the constant possibility of evil and the need to avoid or overcome this. I suppose the problem for theism is not explaining why there is evil and suffering, but why there is no 'intervention' from a deity is supposedly benevolent. I find over many years I cannot believe in a deity who intervenes in the world miraculously to save some and not others. Functionally this means I believe the deity is 'transcendent' and not interfering in the world - like a deist - while my deity is maintaining its fabric (providing the stage but not directing the play).
I can think of various metaphysical and common sense reasons for not supposing a transcendent divinity can intervene in the world. For me any viable understanding or reinterpretation of Christianity must also deny supernatural impositions from outside the cosmos and I have assumed against a future apocalypse that God is waiting to bring (this never ending story of the near ending is getting very tired after 2000 years). However if the divine does not intervene does this mean there is 'no hope' for redemption? Well, perhaps redemption is in the hands of the people properly led by the divine light. Perhaps by utilising some force within the Cosmos, indeed within our selves collectively this will save us in the end from the scourge of death and suffering. And I rather subscribe to Tielhard De Chardin's Omega point notion, and the possibility of final transcendence (the final evolutionary step) via suffering. This is also the way of the Cross of Christianity. Redemption from suffering does not avoid suffering or make suffering 'okay'. Rather something about the world makes evil and suffering inevitable, and ultimately this stems from the cosmos being 'free' and 'independent' of the divine. Good requires the possibility of evil, but not its actuality; there has to be a real choice, a real overcoming, a real evolution of the physical buffeted by the forces of death and decay to arrive at intelligent, creative individuals, with moral sense. Perhaps as in the Eden myth when mankind first developed a strong self consciousness we could have freely chosen the good path while never experiencing evil, and done so indefinitely. But the possibility of evil was always there and eventually finite creatures would push the artificial bounds and choose the 'knowledge of good and evil' but this was also the path not just to folly, but also to wisdom and maturity. So the possibility of natural and moral evil has a cosmic purpose: the separation of the subtle from the gross. By realising our limitation and failure, this should lead not to bitterness and anger, but to realising that we are justing ourselves and our own flaws and disasters by a deep notion of the true, the beautiful and the good, and finding life wanting. The desire for the transcendent in every human breast, is to my mind one of the best 'evidences' of the divine: a lodestone in each one of us that leads us to believe that there is the 'pole' somewhere of goodness to which we should be alligned.