It is sometimes argued that the Incarnation of Christ contradicts the unchangeability of God, for if a divine Person became a man in time, then some change must have occured in the divine Person.
Traditional Christianity, however, has held that God, by definition, is able to act on others without changing. In the divine Logos taking to Himself a human nature, there is no change in his Person, but the created human nature is brought into a new relation with Himself. Hence by the Incarnation there is no change in the Divinity, but only a change in the creature.
As in every single point of theology, these things are far deeper than we realize, and in fact, are ultimately unsearchable in their depths. Learn more about your glorious God: