The reason science cannot explain the existance of God is because scienece is not as clever as it thinks it is.
It cannot explain the so called 'big bang', why it happened, what was here before the big bang... it cannot explain the afterlife... it cannot explain the universe, its expansion or what it is expanding into etc. & for some obscure reason we are supposed to accept that science can answer everything... and if it can't then it doesn't exist... this just shows how minute science is compared to the things it cannot answer.