I am not a philosopher, but it seems to me that the question originally posed, "Do God's energies change?" is one of those questions that always brings us into mystery. That God is immutable, impassible, eternal is universally confessed in the Christian tradition, yet what we mean by these terms is not clear. It is easier to say what they do not mean than it is to say what they do mean.
I have found it helpful to always keep the Christian confession of the creatio ex nihilo
at the forefront. Of course, I have no idea what it means for God to create the world from "out of nothing," but this confession reminds me that God is not a being, even the most powerful being, in the world. How is it even possible to speak of this God who infinitely transcends the world he has created. Every time I open my mouth to speak of God I find that I am almost immediately speaking of him as if he were a being/agent/existent in the world. But he is not. The best Christian theologians, whether Eastern or Western, know this. All of our language breaks down.
The second thing is need to remember is that God created the world in freedom. He did not have to create the world. He does not need the world. If he had never created the world, he would still be the Father, Son, and Holy Spirit in infinite glory, goodness, and perfection. Yet he did create, and so we need to find a way to say that the immutable, impassible, and eternal God "became" Creator, while always recognizing the limitations and inadequacies of this language. The same considerations apply when we speak of God "becoming" man in Jesus Christ. I have found the reflections of the great Reformed theologian, Thomas F. Torrance, who was profoundly influenced by Sts Athanasius and Hilary, to be particularly helpful here:
Athanasius shows that in virture of his intrinsic and eternal Fatherhood, God always had the power to create, and did actually create because he was and is the Father of the Son. God is, and always is, Father, but to create something out of nothing utterly different from himself is an act of his will and freely follows from what he eternally and intrinsically is. Hence, "for God to create is secondary, and to beget is primary" [Con. Ar., 2.2]. ... The truth of the matter, then, is that while God was always Father, he was not always Creator or Maker. That is not to say that the creation was not in the Mind of God before he actually brought it into being, but that he brought it into being by a definite act of his will and thereby gave it a beginning. Quite clearly words like "was," "before," "when" and "beginning" are time-related, and present us with problems when we speak of God, for the time-relations they imply may not be read back into God. These terms have one sense when used of God when they are governed by the unique nature of God, and another sense when used of creatures in accordance with their transitory natures. Thus when the Scriptures tell us that "in the beginning God created" we must understand "beginning" in a two-fold way: with reference to the creating act of God, and with reference to what he has created or his works. Hence Athanasius could say that "while the works have a beginning in being made, their beginning precedes their coming to be" [Con. Ar., 2.57]. Behind the beginning of creation there is an absolute or transcendent beginning by God who is himself eternally without beginning. This is what makes the creation of the world out of nothing so utterly baffling and astonishing. It is not only that something absolutely new has begun to be, new even for God who created it by his Word and gave it a contingent reality and integrity outwith himself, but that in some incomprehensible way, to cite Athanasius again, "the Word himself became the Maker of the things that have a beginning" [Con. Ar., 2.57]. God was always Father, not always Creator, but now he is Creator as well as Father. It is in similar terms that we may speak of the eternal Son who became Man. The Son was always Son of God, but now he is Man as well as God. "He was not man previously, but he became man for our sake" [In ill.om., 3]. ... If God was not always Creator, the creation of the universe as reality "external to God" was something new in the eternal Life of God. If the Son or Word by whom he created all things was not always incarnate, but became man in the fullness of time, then God's communication of himself to us in Jesus Christ who is of one and the same being and nature as the Father, is something new to the eternal being of God. Thus the incarnation and creation together, the latter interpreted in the light of the former, have quite breath-taking implications for our understanding of the nature of God. They tell us that he is free to do what he had never done before, and free to be other than he was eternally: to be the Almighty Creator, and even to become incarnate as a creature within his creation, while remaining eternally the God that he is. (The Trinitarian Faith, pp. 87-89)
I would think that the approach outlined by Torrance provides a way for us to think about the immutability/mutability of the divine energies. And most importantly of all, let us remember that when we speak of the divine essence and the divine energies, we really have no idea whatsoever what we are talking about. All we know is that they belong to the Creator side of the Creator/creature dividing line.