“There was a time when G-d did not have a human nature.” Do you then believe that G-d changed His nature? Or are you speaking only of the human perception of time since G-d is outside of time and space?
In Christian theology, there was a time when God took on a human nature. The Incarnation is seen to be a historic event.
It is an interesting question whether or not God changes his nature. If you compare God walking with man in the cool of the day in the garden in Genesis, with God at the end of the Biblical period in the writings of Daniel, it is hard not to see a lot of character development on behalf of God too.
God does change his mind constantly in the Old Testament at least. In the New Testament, this reaches an ultimate state of God becomes man.
I am open to the idea that God changes his nature, that even God develops. Certainly in Catholic theology, the idea of Jesus being perfected by suffering accepts that dynamic.
On the other hand, God as alpha and omega, as he who is and was ahd shall be ‘all at the same time’ so to speak does not necessarily require one to believe that God must have changed his human nature when he took on a human nature. God transcends time. While human nature has not evolved in which a state of affairs outside of time is within our ability to perceive, science is aware that time and space themselves are relative to one another and not absolute states of being.
Existence outside of time therefore is logically possible, even if beyond human perception.
And God certainly has that aspect to his nature that a human cannot, since we live within certain limits. But Creators are not, even cannot be, likewise limited to the dimensions of their creation.
Nevertheless, God also limited himself to the dimensions of human experience when he took on human nature in 1 CE. “Became lower than the angels” is how the early Fathers speak about that personhood of God.
Therein lies the paradox that lies at the heart of Christianity, and at the heart of the question of this thread too. To describe God, one is conceiving a being of such a magnitude of greatness that no other being greater could exist. And yet when it comes to some of the highest virtues that exist, such as courage and hope and faith, these virtues require limitations to power and knowledge in order to become realized. Even love and compassion are magnified in the face of suffering.
So, by definition, a Being that which none greater can be conceived, must accept being limited in order that greatest virtues conceivable are indeed a part of his nature.
One of the miracles attested to of saints such as Martin de Porres is bilocation. Whether or not someone accepts such miracles as factual, indeed this sort of attribute of being two persons at once becomes necessary to describe the nature of God. The Creator in effect surpassed himself through his creation. We indeed do glorify God in our own beings, for it is the very act of creating us that the fullest measure of the greatness of God is realized, not just in the mind of God, but in reality of his living through us, the veritable crown of his creation.