The doctrine of the Triune God is taught throughout the ENTIRE Bible - both the Old and New Testaments. Here are a few sites that demonstrate that Scripture DOES lay out the doctrine quite well:
The Biblical Doctrine of the Trinity
It is undeniable that from the very start the first Christians were taught the truth of the Trinity and that Jesus, as the Son of God, is the second person of the Trinity. What the church did at Nicea was to condense the doctrine into a creed format that was useful for believers to memorize and to be able to continue to teach that truth. It did NOT, however, take the Christian church that long to "come up with" the doctrine - it had been taught and believed from the start.
******The doctrine of the Triune God is taught throughout the ENTIRE Bible -******
So, then the Jews believe in the Trinity based on the Old Testament?
As for Christians being taught the Trinity from the beginning. I think you are wrong about that. We can certainly see the elements are there, but in all the writings of Paul, he never it tied together.
I think the doctrine became clear as God revealed it over time as the questions came up regarding how Jesus was God and whether the Holy Spirit was God.