It is true that God cannot die. It is also true that man can die. But Jesus has two natures, not one. It was the human part of Jesus that died on the cross...
not the divine. But, because He is both God and man in one person, and because He was sinless, His sacrifice is sufficient to cover the sins of the world...
Does this seem like a reasonably possible explanation to you?
If the person asks where's the proof for God/Jesus/Christianity, go here.