To say that God is unchanging does not do full justice to the rich doctrine of the Holy Trinity in Christian theology. God is dynamic; God is a living God. The demonstration of this is in the relationships between the Persons of the Holy Trinity, which form an eternal procession from the Father to the Son and to the Holy Spirit. This description is recognized in the early creeds of the church.
It is one thing to assert that time is real to God; it is quite another to put time back of God. When this is done, as with the process theologians such as A. N. Whitehead, we have a view that places God in an ongoing process of creation, and also in the struggle with evil. Such a view has the advantage that it resolves the 'creation-evolution' controversy by seeing God as a continuous, participatory Creator. However, this view contrasts sharply with the Genesis account, which declares the original world to be "very good". It didn't need any more 'tweaking' after its origin.
We, creatures as we are, do not fully comprehend time. We do not understand fully the relationship between time and eternity, between God's time and our time. Augustine pondered this matter 1600 years ago, and not much further penetration of the matter has occurred since then. So we should not be hasty to render judgement against process theology, or evolutionary creation views, since we really do not understand clearly the mystery of Creation: how the transcendent, eternal God interacts with the temporal world. All we can do is define the boundaries of orthodoxy, by affirming that the world was created good, that evil is temporary and good will ultimately triumph, because God is good.