This conversation is only going on, as it has been for ever and a day, because of the presumption, theologically built into all Christian/Judeo teaching and tradition, whether fundamentalist, orthodox or otherwise, that a fully demonstrable proof, one that meets all Enlightenment criteria is not possible. Ironically science shares this opinion with religion!
But lets start with a definition: The only truly definitive proof of God would be by a path of faith 'revealed' by God which is then confirmed by God in a direct, irrefutable intervention into the natural world. Few would dispute this in principle. Well that seemingly impossible principle has now happened! And there could be a lot of theological gnashing of teeth in the near future.
The first wholly new interpretation for two thousand years of the moral teachings of Christ has been published. Radically different from anything else we know of from theology or history, this new teaching is predicated upon the 'promise' of a precise, predefined, and predictable experience of transcendent omnipotence and called 'the first Resurrection' in the sense that the Resurrection of Jesus was intended to demonstrate Gods' willingness to reveal Himself and intervene directly into the natural world for those obedient to His will, paving the way for access, by faith, to the power of divine Will and ultimate proof!
Thus 'faith' becomes an act of trust in action, the search to discover His 'Word' of a direct individual intervention into the natural world by omnipotent power that confirms divine will, law, command and covenant, which at the same time, realigns our mortal moral compass with the Divine, "correcting human nature by a change in natural law, altering biology, consciousness and human ethical perception beyond all natural evolutionary boundaries." So like it or no, a new religious teaching, testable by faith, meeting all Enlightenment criteria of evidence based causation and definitive proof now exists.
Nothing short of an intellectual, moral and religious revolution is getting under way. I've started testing this new teaching for myself. And testable truth trumps all opinion. However ancient, learned, scholastic or otherwise. To test or not to test, that is the question and the measure of noble hearts? For more info Google: The Final Freedoms