In Trinitarian thought, God has one will and one action. Everything is accomplished by the Three Persons of the Trinity acting in unity. This applies to creation as well. The typical language is along the lines of 'The Father created through the Son in the Spirit', but there is always an emphasis that the Three Persons act in unity.
Concerning creation St Athanasius uses this unity of action in creation as a defense of the divinity of both the Word and the Spirit. In his first letter to Serapion he writes
The Son, like the Father, is creator; for he says: ‘What things I see the Father doing, these things I also do’. 'All things’, indeed, 'were made through him, and without him was not anything made’.
But if the Son, being, like the Father, creator, is not a creature; and if, because all things were created through him, he does not belong to things created; then, clearly, neither is the Spirit a creature.
For it is written concerning him in the one hundred and third Psalm: 'Thou shalt take away their spirit, and they shall die and return to their dust. Thou shalt put forth thy Spirit, and they shall be created, and thou shalt renew the face of the earth’.
As it is thus written, it is clear that the Spirit is not a creature, but takes part in the act of creation.
The Father creates all things through the Word in the Spirit; for where the Word is, there is the Spirit also, and the things which are created through the Word have their vital strength out of the Spirit from the Word.
Thus it is written in the thirty-second Psalm: 'By the Word of the Lord the heavens were established, and by the Spirit of his mouth is all their power
The Church Fathers often speak of this unity in action, but usually it is in the context of redemption or the arrival of the Spirit at Pentecost instead of creation.
Pope Leo the Great wrote in Sermon 77 on Pentecost
For the Majesty of the Holy Ghost is never separate from the Omnipotence of the Father and the Son, and whatever the Divine government accomplishes in the ordering of all things, proceeds from the Providence of the whole Trinity. Therein exists unity of mercy and loving-kindness, unity of judgment and justice: nor is there any division in action where there is no divergence of will. What, therefore, the Father enlightens, the Son enlightens, and the Holy Ghost enlightens: and while there is one Person of the Sent, another of the Sender, and another of the Promiser, both the Unity and the Trinity are at the same time revealed to us, so that the Essence which possesses equality and does not admit of solitariness is understood to belong to the same Substance but not the same Person.
St Ambrose in his treatise On the Holy Spirit wrote
But the Holy Spirit also was given, for it is written: I will ask the Father, and He shall give you another Paraclete. And the Apostle says: Wherefore he that despises these things despises not man but God, Who has given us His Holy Spirit. Isaiah, too, shows that both the Spirit and the Son are given: Thus, says he, says the Lord God, Who made the heaven and fashioned it, Who established the earth, and the things which are in it, and gives breath to the people upon it, and the Spirit to them that walk upon it. And to the Son: I am the Lord God, Who have called You in righteousness, and will hold Your hand, and will strengthen You; and I have given You for a covenant of My people, for a light of the Gentiles, to open the eyes of the blind, to bring out of their fetters those that are bound. Since, then, the Son is both sent and given, and the Spirit also is both sent and given, They have assuredly a oneness of Godhead Who have a oneness of action
This continues to to be the traditional understanding of the Trinity.
Much more recently, St John (Maximovitch) of San Francisco wrote
Men have also one nature. But whereas God is a Trinty One in Essence, in men there constantly occur divisions.
In Father, Son, and Holy Spirit there are One Thought, One Will, One Activity.
What the Father desires, that also the Son desires, and that the Holy Spirit desires. What the Son loves, that also the Father loves, and the Holy Spirit. What is pleasing to the Holy Spirit, is pleasing also to the Father and to the Son.
Their Activity is likewise one, everything is done jointly and harmoniously.