Logic and physical realms do not work in proving God period.The only proof is subjective he is all the subjective ,you cannot prove scientifically that a flower is beautiful,you have to see it ,it cannot even be explained or assumed by logic that flowers must be beautiful ,its a very private experience that is real however not physically ,it isn't imagination but a real common experience of reality that we feel intelligence in life.If you believe in logic or physical proof only then you don't know God.