it never existed. But I think it was invented in the 3rd Century

This is the nature of almost all "answers" about religious doctrine.

… and now, Father, glorify me in your own presence with the glory which I had with you before the world was made.

Notice, before the creation, the Son was “with” the Father. Also, the Son addressing the Father and himself in an “I/thou” relationship is unmistakable. We have distinct persons here. “Father” and “Son” reveal a generative relationship as well. Yet, this relationship between two persons clearly has no beginning in time because it existed before the creation, from all eternity. Thus, the relational distinction is real, and personal, but as far as nature is concerned, Jesus’ words from John 10:30 come to mind: “I and the Father are one,” in that they each possess the same infinite nature.

Not until the Council of Nicaea. Nicene Creed and then:


With this declaration in 381, which would become known as the Nicene-Constantinopolitan Creed, the Trinity as generally understood today became the official belief and teaching concerning the nature of God

From the very beginning of the church, Christians have understood the mystery of the Trinity, even before they began using the term Trinity.

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More

Council of Nicea 325 ad affirmed existence of Trinity.

Nor have any solo members of the group existed either.

I love the irony of the three when believers proclaim monotheism. It always reminds me of the old country song, "I'm my own Grandpa."

teaching that it started on the wall of a cave.

What about, can the guy make coins appear? If so, I wanna be his bff.

If the nature of God is tripartite, that nature must be eternal. A infinite-limitlessness can not be 'sometimes this' and 'at no time that'.
The vastly different natures of the biblical god-father and the god-son are seen in the wrathful vengeance of God vs the love from God.
Which nature is absolute and existent before, during, and after creation?

Attributes, qualities, adjectives are meant to distinguish one thing from another thing on the same order of reality; the red rose flower, not the lilac colored lily flower.
A 'one and only God' can-not-be compared to another 'one and only God.

God may have an essential nature, a irreducible identity*, but no qualities or attributes.
Indeed all that exists must essentially borrow 'existence' from the pre-existent.
Assuming that by God we mean a 'conscious-being', then our own 'conscious-existence can not be separate from that.

* Some posit that the essential nature of Divinity is a trinity of "Existence-Consciousness-Limitlessness"; a blissful-being, unlimited by any 'otherness' that could constrain the joy.

Homework challenge: Negate your own conscious existence. Show your work.

John I says: "In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. ... The Word became flesh and dwelt among us." As I understand it, this means that the Logos, "Word," means Jesus, the pre-existent second person of the Trinity. So God would have had to have created himself. The early Greek Christians who were trying to establish a coherent belief system had to consider the fact that if they deemed Jesus to be a god they wouldn't be monotheists any more, so they had to come up with a concept that Jesus, God and the Holy Spirit (which is a thing in Judaism, the influence of God over the world) were all one entity. Jesus had to be God or the concept didn't work, but Jesus didn't exist in the world until he was born as a human, then died (sort of) and went back to being pure God again.

No, I don't get it either.

We all have a soul, but the human body will die while the soul lives on.

Many earlier religions were Matriarchial and the 'trinity' was Maiden/Mother/Crone

The Father is male.
The Holy Spirit is female.
The Son is their children.
It was presented this way so people could grasp the idea of creation as a process that they are part of; so they could link their physical life with their spiritual life.
In this simplistic form, it acknowledges the spirit within each of us.