We cannot speak of God creating any part of himself, but God does progressively reveal himself, to humanity and even to his own self. The Trinity is three divine persons, Father, Son, and Holy Spirit. Not three Gods, but three divine persons, the three of which constitute the one God. The Trinity of God is a mystery—not fully understood, and incapable of full understanding by any human. The Son of God is begotten of God the Father, the Holy Spirit proceeds from both, and all three had their first revelation as Godhead.
Godhead is undifferentiated, unexpressed, absolute and singular being. Godhead is the simple, essential, unified, core God. Godhead is the necessarily first and fundamental revelation of God. Every movement of God — every act of thought, will and love further reveals and defines God. “When” Godhead acts in such a way as to reveal the divine Son, Godhead reveals himself to be God the Father. God makes revelation simply by thinking or willing ― when God thinks of himself, his image the Son of God is revealed.
The revelation of Godhead as the three distinct persons of the Trinity is thought to be non-optional. “When” Godhead thinks, he “first” thinks of himself, (what else, no creation yet).
In doing so, Godhead reveals the trait of intellect, beyond the trait of pure being of the Godhead. When Godhead thinks of himself, he generates the complete image of himself who is the Son of God; and Godhead is now God the Father. The Son of God is the fullest expression of God. The Son of God himself is not yet fully revealed; the human children of God are called to be yet more expression of the Son of God, as the body of Christ.
Godhead which is the essence of God, necessarily remains in the three persons who are God: Father, Son and Holy Spirit.
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The Father and the Son directing their wills toward each other generates the Holy Spirit. The Holy Spirit may be thought of as the bond of love (commitment) between the Father and the Son. In example, think of two people having a common pursuit; this might be marriage or a business perhaps. As this pursuit is cultivated it becomes a real separate entity, this third entity becomes more than words. A marriage or a corporation is given a certain legal status and rights of its own. The efforts of the two people give real form to the third entity.
This example is necessarily inadequate. When God thinks and wills however; it is as real as it gets. The love of the Father and the Son toward each other is divine, selfless, full, intense, real, and permanent. Included in these thoughts is the possibility of creation outside of God. The Holy Spirit who results is divine, independent, full, intense, and permanent.
The Holy Spirit is the acting agent of creation, sent by the Father and the Son, and is a real and complete divine person.
The Holy Spirit is the result of the mutual willing of the Father and the Son. The Holy Spirit is not necessarily God’s proportional will. It is possible, even likely that the Holy Spirit is God’s compete, but weighted will, with favoritism toward mercy, joy and peace.
The Holy Spirit is not just the mutual will of the Father and the Son; the Holy Spirit is a distinct divine person of the Trinity. The Holy Spirit acts freely (within the bounds of divine perfection). The Holy Spirit is not just the result of love, but is a proactive lover. The Holy Spirit is not just the result of the mutual participation of the Father and the Son, but is himself a participant in the Father and the Son.