It seems to me that we cannot prove (or finally disprove) the existence of deity by reasoning from either pure logic or the natural world, while our mystical experience is unrealisable. Therefore we have no certain knowledge of any deity. At best we are left in a fog of agnosticism and uncertainty, while for many we should not believe in anything without adequate evidence, which dictum requires at least a practical atheism.
However the failure of reasoning and experience do not exhaust the truth claims of many religions. In particular there are a number of religions that claim to have been based on the deity's revelation to various people, in sundry times and divers manners. Christianity in particular insists that the deity has revealed itself and it is this 'revelation' that a person is called to believe in, not any reasoning or experience. The ultimate revelatory event for Christians is the person and life of Yeshua of Nazareth, called the Messiah or Christ. A belief or rejection of Christianity requires an assessment and decision about this revelation.
But how do we know a claimed revelation is 'true' and really from a 'deity' demonstrating that deity exists? On the face of it, we would have to reason about who is making the claim and their reliability and the general coherence and back story. But I am beginning to suspect that Christianity demands not a rational consideration and assent but that faith is a non rational, emotional or 'heart' response to the revelation. Either we are individually and emotionally driven to believe or not as the case might be. "Let those who have ears to hear"...indeed. I am therefore inclined to think that not everyone is able to believe by virtue of their mental disposition and that faith is a gift. But if this is so then we are not 'free' to choose to believe or not. There is plenty of biblical evidence that supports a theology that emphasises divine sovereignty - divine determinism, while this is contrary to most human notions of fairness and justice.