The Trinitarian concept is just that-- a concept. It is an attempt to try and possibly explain the relationship of Jesus and the Holy Spirit with God using the verses within the Gospel.
A key to understanding this approach is to also try and understand the use of "essence" brought forth to us by the ancient Greeks prior to Jesus being born, especially Aristotle and Plato. We gotta remember that the NT was written in Koine Greek, especially for Church in the diaspora, so they would be familiar with using this approach.
Here:
Essence - Wikipedia
A more sceptical view of this "Trinity" given its role in fomenting strife and division amongst all classes of Christians is that the Trinity is not an attempt to explain anything, but an invidious conflation of the triad philosophies of Plotinus, Porphyry, Iamblichus and Ammonius Saccas (founder of the Neoplatonists - 3rd century AD) with Christian theology for the sake of politcal one-upmanship.
The concept of the "homoousios" is central to philosophical triadism.
Two ancient documents disclose the origination of the homoousios in pagan philosophy and its links to later Christian theology. One is the Poimandres, the first tractate in the Corpus Hermeticum, a body Hellenistic Gnosticism dating back to 1st century BC. A second is the Anonymi Monophysitae Theosophia - 6th century AD - which seeks to reconcile pagan philosophies with Christian doctrines.
A sketch of the pagan philosophy is as follows (Pier Franco Beatrice's article
The Word "Homoousios" from Hellenism to Christianity)
In the course of the relevation to Poimandres, Hermes learns that the Nous (mind) is the supreme God and the Logos (word) that proceeds from him is the son of God. Poimandres goes on to reveal that the Nous, who is the androgyne supreme God, by speaking, generated a second Nous, the Demi-urge, god of the fire and spirit, who crafted the seven archons that encompass the sensible world; and that their government is called fate.
The Logos, Son of God, from the elements that fall downwards, leapt up to the pure craftwork of nature and united with the Nous-Demiurge "because he was of the same substance" (homoousios).
The application of the term "Logos" is further divided between the Nous of the highest power (the supreme God), which is denoted as the "Logos of sovereignty," and the Pneuma. So Logos is something of an ambivalent term.
The concept, if not the term homoousios, characterizes the overall Hermetic conception of the Godhead.
The Poimandres along with other Hermetic tractates, elaborates with the support of Hellenistic philosphical terminology, the pagan doctrine of the Egyptian priests circulated under the name of Thoth-Hermes. In Egyptian religion, the Nous-Demiurge is called by different name Amum, Ptah and Osiris.
The Pneuma was identified by the Eqytians with Amum or Zeus. The Pneuma as a fine breath of the Nous, hovered over the waters of chaos before creation, whilst the Nous is associated with the "essence" of God.
In the Anonymi Monophysitae Theosophia, five Eqyptian oracles proclaim the Nous or supreme God (also called Logos) and his son the Logos share divinity with the Pneuma.
