Genesis says that in the beginning, God spoke, and by speaking brought everything into existence, and the Spirit hovered over the waters. The Speaker, the Spoken, and the Spirit are not part of the creation, so taken together, they must be God. John’s gospel takes it from there and says that the Word became flesh in Jesus Christ. That brings the terminology of Father, Son, and Holy Spirit to the Trinity, because in the legal context of John’s writing, the Father is the proprietor and the Son holds the Father’s power of attorney. Everything Jesus says is a divine word, everything that Jesus does is a divine act.
These assertions quickly led to an articulate doctrine of the threeness-in-oneness of God. The New Testament writers, in particular John, trace the divine triunity back to Genesis by identifying Jesus as the Word of God through whom all things were made. In Genesis 1:1‑3, God speaks the world into existence out of nothing, and the Spirit of God hovers over the water. The Speaker, the Spoken, and the Spirit are uncreated, they exist before creation, but the only thing that exists before anything is created is God.
The concept of the Trinity precedes the terminology. Ancient writings going back at least to Ignatius, a bishop who was born in AD 33, say that Jesus is God, that Jesus’ heavenly Father is God, and that the Holy Spirit is God, but they also maintained that there is only one God. The word “Trinity” is a Latin word that was coined by Tertullian in the second century, which rapidly replaced the older Greek term “triad” because the word “Trinity” means “tri-unity” and is more accurate.
The biggest mistake we make today is to think of the Trinity as something to understand rather than as a set of rules for thinking and talking about God.