Was the child Jesus God is more proper in context.
Is it possible for God to grow in wisdom and stature?
LUKE 2:52 And Jesus increased in wisdom and in stature, and in favor with God and man.
In his human nature, yes.
And the answer is yes. As your question that follows indicate:
Is it possible for God to grow in wisdom and stature?
No, it is not possible. He Is God in Mary's womb, and in the manger, and att all points in time. It is the human nature of Jesus that went through the human process of maturing. Jesus would not be fully human if He bypassed some of the natural human experience. He also, for example, prayed to God.