Are Origen's and Calvin's views on God compatible?

Origen's View on God

Origen of Alexandria (185-232) was a great Bible scholar and an influential early Christian theologian whose contributions has been underappreciated, mostly because he was posthumously declared heretic by Emperor Justinian in AD 543 and because works derived from some of his teachings were anathematized by the Second Council of Constantinople in AD 553. However, none of the ten propositions condemned in 543 were about the nature of the Trinity.

In the development of the Trinitarian doctrine which culminated in the Nicene creed promulgated at the AD 325 First Ecumenical Council of Nicaea, Origen's view represented an early 3rd century A.D. major development of the Trinity but still not the fully developed early 4th century A.D. shape. He, along with his contemporary Clement of Alexandria (150-215), were battling Gnosticism in Alexandria and attempted to use middle Platonism fashionable in Alexandria at the time to defend the Orthodox understanding of God, Jesus, and the Holy Spirit. Although the resulting trinitarianism was flawed, it was still a step in the right direction [see [1] pages 10-11].

From a paper on the Historical Development Of the Doctrine of Trinity (emphasis mine):

In Clement’s trinitarian construct, God the Father is absolutely transcendent, ineffable and incomprehensible; He is unity, but beyond unity, and transcending the monad, and yet embraces all reality. The Father can be known only through His Word (Logos), or Son, who is His image and inseparable from Him, His mind or rationality. Like the Nous of mid-Platonism and of Neo-Platonism, the Word is at once unity and plurality, comprising in Himself the Father’s ideas, and also the active forces by which He animates the world of creatures. His generation from the Father is without beginning (the Father is not without His Son; for along with being Father, He is Father of the Son); and He is essentially one with Him, since the Father is in Him and He in the Father. The Spirit, thirdly, is the Light issuing from the Word, which, divided without any real division, illuminates the faithful; He is also the power of the Word which pervades the world and attracts men to God.

Thus, pursuant to his Platonic Christian theism, Clement presents a graded hierarchy of a triune but one God in which the Son is subordinated to the Father, and the Spirit subordinated to the Son. Notwithstanding, no inequality seems to be implied, since Clement and Origen set out to develop an orthodox Gnosticism in place of its heretical forms pervading Alexandria through the Gnostic teachers – Basilides, Carpocrates, and Valentinus. Similarly, J.N.D. Kelly asserts that Clement and Origen were profoundly enamored to understand the triune Godhead in the light of middle Platonism fashionable in Alexandria in the time. But it is Origen’s radical popularization of the same kind of Clementine trinitarianism that would lay the foundation for the most notable Christian trinitarian controversies.

Origen's trinitarianism is described at SEP History of Trinitarian Doctrines as follows:

... These late second and third century authors use such terms not to refer to the one God, but rather to refer to the plurality of the one God, together with his Son (on Word) and his Spirit. They profess a “trinity”, triad or threesome, but not a triune or tripersonal God. Nor did they consider these to be equally divine. A common strategy for defending monotheism in this period is to emphasize the unique divinity of the Father. Thus Origen (ca. 186–255),

The God and Father, who holds the universe together, is superior to every being that exists, for he imparts to each one from his own existence that which each one is; the Son, being less than the Father, is superior to rational creatures alone (for he is second to the Father); the Holy Spirit is still less, and dwells within the saints alone. So that in this way the power of the Father is greater than that of the Son and of the Holy Spirit, and that of the Son is more than that of the Holy Spirit… (On First Principles 1.3)

Many scholars call this strain of Christian theology “subordinationist”, as the Son and Spirit are always in some sense derivative of, less than, and subordinate to their source, the one God, that is, the Father. One may also call this theology unitarian, in the sense that the one God just is the Father, and not equally the Son and Spirit, so that the one God is “unipersonal”.

Calvin's View on God

Your quote comes from Calvin's magnum opus Institutes of the Christian Religion, Book I, Chapter 13 titled "The Unity of the Divine Essence in Three Persons Taught, In Scripture, From the Foundation of the World", section 25, which is in the middle of sections 21-29 where he refuted a variety of objections to the true doctrine of Trinity.

Rather than analyzing the specific view rejected in section 25, let's simply consider Calvin's view of God, which of course is the fully developed Trinitarian understanding of the Nicene creed, which defines the Trinity as follows:

We believe in one God,
  the Father almighty,
  maker of heaven and earth,
  of all things visible and invisible.

And in one Lord Jesus Christ,
  the only Son of God,
  begotten from the Father before all ages,
       God from God,
       Light from Light,
       true God from true God,
  begotten, not made;
  of the same essence as the Father.
  Through him all things were made.
  For us and for our salvation
       he came down from heaven;
       he became incarnate by the Holy Spirit and the virgin Mary,
       and was made human.
       ...

And we believe in the Holy Spirit,
  the Lord, the giver of life.
  He proceeds from the Father and the Son,
  and with the Father and the Son is worshiped and glorified.
  ...

For proof that Calvin subscribed to the Nicene creed, see article 5 of the A.D. 1559 French Confession of Faith composed by him:

We believe that the Word contained in these books has proceeded from God, and receives its authority from him alone, and not from men. And inasmuch as it is the rule of all truth, containing all that is necessary for the service of God and for our salvation, it is not lawful for men, nor even for angels, to add to it, to take away from it, or to change it. Whence it follows that no authority, whether of antiquity, or custom, or numbers, or human wisdom, or judgments, or proclamations, or edicts, or decrees, or councils, or visions, or miracles, should be opposed to these Holy Scriptures, but, on the contrary, all things should be examined, regulated, and reformed according to them. And therefore we confess the three creeds, to wit : the Apostles’, the Nicene, and the Athanasian, because they are in accordance with the Word of God.

Conclusion

Origen's and Calvin's views on God are compatible in that both affirm monotheism and the pre-existence of Jesus (as the Logos) and the Holy Spirit, but Calvin's view is of course the more fully developed doctrine of the Trinity, defined since AD 325, in that the subordinationist defect has been eliminated.

References

1. The Historical Development of the Doctrine of Trinity, a paper by Samuel Japhets for History of Christianity I, Liberty University, 2017
2. Stanford Encyclopedia of Philosophy article History of Trinitarian Doctrines
3. Nicene Creed