Your claim about the early Church's belief in the Trinity is directly contradicted by the Stanford Encyclopedia of Philosophy: "No theologian in the first three Christian centuries was a trinitarian in the sense of believing that the one God is tripersonal, containing equally divine 'persons,' Father, Son, and Holy Spirit."
Ah, here you've skipped over 'in the sense of' in the above quote.
The New Testament is tri-personal, and the three persons are divine, the nature of their relation is not explicitly stated.
The Church was tri-personal in its baptismal formulae and its confession, from the earliest writings of the post-Apostolic era.
Pope Clement of Rome – in his Epistle to Corinth perhaps as early as 70CE but no later than 96CE – says: "Do we not have one God, and one Christ, and one gracious Spirit that has been poured out upon us, and one calling in Christ?" (1 Clement 46:6).
Ignatius of Antioch, writing around 110CE, says: "Christ, and to the Father, and to the Spirit" (Letter to the Magnesians VIII).
Justin Martyr (100-165) is the first to use much of the terminology of Trinitarian theology – the Father and the Son as the same
ousia and yet are also distinct
prosopa, anticipating the three persons
hypostases of Tertullian (who used the Latin
substantia), and Origen.
For many of the early Fathers, there was just one
hypostasis in God, and the terms
ousia and
hypostasis were treated as synonyms, only later attaining concise distinction and subsequently declared at the Council of Chalcedon in 451CE.
Nevertheless, the church was tri-personal from the get-go.
The first
mention of 'trinity' first appears in the Greek of Theophilus of Antioch (died 183-5CE) in
Theophilus to Autolycus
"In like manner also the three days which were before the luminaries, are types of the Trinity (Τριάδος /
Trinitatis) of God, and His Word (Λόγου
/ Verbi), and His wisdom (Σοφίας
/ Sapientiae)."
The commentary adds: "Τριάδος. The earliest use of this word “Trinity.” It seems to have been used by this writer in his lost works, also; and, as a learned friends suggests, the use he makes of it is familiar. He does not lug it in as something novel: “types of the Trinity,” he says, illustrating an accepted word, not introducing a new one. An eminent authority says, “It is certain, that, according to the notions of Theophilus, God, His Word, and His wisdom constitute a Trinity; and it should seem a Trinity of persons.” He notes that the title σοφία, is here assigned to the Holy Spirit, although he himself elsewhere gives this title to the Son (book ii. cap. x., supra), as is more usual with the Fathers.”
The first
defence of a doctrine was by Tertullian, in
Contra Praexeas, written around 213CE.
"Chapter II—The Catholic Doctrine of the Trinity and Unity, Sometimes Called the Divine Economy, or Dispensation of the Personal Relations of the Godhead."
For sure this defence was of a doctrine that was subsequently abandoned, it's not the doctrine of the Cappadocians, but my point is to show that the idea of a Trinity of Persons was indeed around in the first Christian centuries, but had yet to be
dogmatically declared as three persons of equal stature in every degree.