How even one objection from a Muslim against Christianity, refutes Islam: "How can God die on the cross?"

The Muslim objection: “How can God die on the cross?” does not make sense in the first place, unless Muslims are willing to concede that God can possess a human body in which to die. They would then be arguing that human body cannot die. But then if that human body could not die, how would it exactly be human? Wouldn't it be more like the invulnerability of superman? And how do they argue God cannot die, when they argue God cannot be God and more than God (human) in the first place?

I find this question problematic from a Muslim perspective. According to Islam, wouldn't God have died, when he became human, meaning God ceased to exist, when he transformed into a human, so why is the referenced objection specifically God died on the cross? This presupposes Jesus could of been God and human all the way up until his death on the cross. So do you believe it’s possible for Jesus to be God and Human, and if you don’t, why then make the specific objection that God only died upon the cross? unless you are presupposing the Hypostatic Union? (the two natures of Christ: God and Man).

Can Muslims explain specifically if the Creator stopped existing after his last breathe on the cross, why according to you did the Creator not stop existing before this point such as when he became incarnate? Or are you conceding the Creator can be God and Man? And therefore you don’t object to the incarnation, but only the incarnate ones death? Why are you arguing God died on the cross as opposed to God died at his incarnation, unless you agree with the Christians, Jesus can be God-man?

Is it not true that when God was conceived in the womb of Mary and later given birth by Mary, that is the exact moment that Muslims argue God ceased to exist since according to Muslims God cannot be God and Human. For God to exist as a human, means he no longer exists as God, yes?

However if a Muslim argues that God died on the cross, then they are indirectly admitting, God can be God and Human prior to the cross, as Jesus exists as both God and Human.

But if God can be God and Human (before the cross), then surely the objection that God died on the cross is also refuted, since God’s humanity was crucified not his divinity.