Agree 100% with what you said, but I dont think it addresses the question.
Why do sola scriptura protestants believe in the Trinity? Answer: because they are not really sola scriptura
Good point.
I heard an evangelical once say that the Trinity is taught in the scriptures, but not defended in the scriptures. I think that is true.
So, this means the Trinity can be inferred by means thorough study of scriptures. However, thorough study requires a long time, and also requires a complete collection of biblical manuscripts at hand.
Now, what I find interesting is that, nevertheless, belief in Jesus as God existed in the writings of Ignatius about the year 110, well before there could have been much systematic exegesis of NT scripture. Even if all NT scriptures were available to the researcher, which they could not have been, since agreement on what NT scriptures actually were, was several centuries away.
So, if not through scriptural exegisis, how could the early Christians believe in the deity of Jesus? It could only be through traditional apostolic teaching. That is, Jesus’ divinity (and that of the HS) was taught orally by the apostles and their successors verbally to the churches. The early Christians did not, and could not, read their bibles to find this out! In other words, the early Chrisitans were not sola scriptura. It would have been impossible for them to be that way.
However, since later Christians had the correct apostolic teaching regarding Jesus, they were subsequently able to correctly understand the NT scriptures in regards to Jesus.
Unfortunately, many of those who in later centuries rejected the idea of apostolic tradition, and consequently did not have benefit of it, relying only on scripture, have come up with all sorts of ideas of who Jesus is. Some of them deny Jesus’ divinity, such as Unitarians and Jehovah’s Witnesses. Some, by going by bible only, even say He is Michael the Archangel! Some say He wasn’t even bodily resurrected. And so on.
In summary, for those who already know that Jesus is God, and the Holy Spirit is God, see the Trinity clearly in scripture. But, for those who don’t have that prior knowledge, the ignorant, it is not at all clear.