Just as Jesus did not stand up in the manger and announce his divinity, God did not stand on Mt. Sinai and give a theological exposition of the three distinct Persons who exist consubstantially and eternally. God is like a good teacher, who reveals his truth gradually, planting seeds, and evoking the truth of the conclusions from his students. We see Jesus doing this with his apostles in Matthew 16, when he asks them who he is.
A college professor of mine once said to be leery of someone who tells you everything about himself in the first five minutes you know him. Jesus did not do this, and neither has the Father.
In the Old Testament God needed to establish monotheism for the Jews to make them stand apart from all the polytheistic religions that abounded. Monotheism was almost unheard of, and if Yahweh had tried announcing that he is three Persons the people of the day might have misunderstood it as Tritheism, which is a heresy.
Today, we have enough trouble trying to get people to believe in the one true God, let alone many. Thus the New Testament was a better time for God to have revealed his true nature, now that the danger of a polytheistic misunderstanding had been eliminated.