The only person who knows for certain that something is real is the person who witnesses it (and even then the truth of the situation is subject to that individual's interpretation). This is true of the empiricism of science as it is for any other human endeavour. The level of our belief in anything is based on our faith in the witness(es) to events that we have not witnessed ourselves. Do we trust their veracity?
Orthodox Christianity is based on the realities of the Christ event relayed to us from the accounts of the original witnesses, not on the suppositions from out of the subsequent Christian tradition. That Christ rose from the dead is a scientific claim not a religious claim - a claim we believe or not depending on our faith in those witnesses.
It is totally wrongheaded to claim that the existence of God cannot be proved unless we accept that the existence of anything not witnessed by ourselves cannot be proved. For orthodox Christians the existence of God has been proved in Christ (a point Christ himself majors on in the Gospel record). An intelligent Christian will accept that it is possible that the witnesses were wrong and that God does not exist. An intelligent scientist will accept that the Big Bang theory may turn out to be completely or partially wrong. But the Christian chooses to believe in God and the scientist chooses to believe in the Big Bang because of their faith in the witnesses to the empirical.
God is either an observable fact or is non-existent.