I think that, when the formualtion of the Trinity doctrine was coming to be, it was ebecause of the issue of referenincing OT passages with NT passages.
The people of that time, typiclaly "reformed Jews" and "reformed pagans", were struggling with the concept of a Divine Jesus and he he relates to His Father and how that effected the passages in the OT or better the Old Convenant.
EX: In the Old convenant Gos is the only one that forgives sins, that reedems, that Judges, but in the New Covenant that role ( amongst many others) is applied to Jesus.
Does that make Jesus God? does it make him THE God ?
The Trinity was a way on interpreting that relationship between God, Jesus and the Holy Spirit, for it seemed that in this New Convenant, when COMPARED to the Old, there was some "intermixing, and as we can imagine for the Jews of that time, some confusion.
Jesus being God "solved" that problem, even if it was not entirely scriptural.
The Fact is, with the New Covenant Jesus became Saviour, Redeemer and Judge, because his Father willed it so, because that is how it had always been, since the beginning. Jesus didn't had tp be God, he is all the God is for he is the full manifestation of God.