I think biblical evidence of divinity would be prayer and worship. Scriptures indicate the apostles prayed and worshiped both God the Father and Christ the Son. However, I know of no such scripture concerning the Holy Spirit.
Never-the-less, having established in scripture that God and Christ were divine, reconciling monotheism with God and Christ was necessary.
I believe there is a sufficient body of scripture to establish that the apostles understood God and Christ to somehow be one in the same and that there was no conflict with monotheism. However, I don't find where they had a clear understanding of the nature of the Holy Spirit. Was the Holy Spirit a diety, or some sort of force/presence? New Testament writers are not clear on that.
“New Testament writers are not clear on that.”
To believe that reveals a lack of familiarity those writers.