The Holy Trinity’s reality is apparent throughout Scripture.
The TERM came in later as the Doctors of the Church drew a conclusion from scriptural study that the Lord is three persons in one God.
Well put.
The word games which are at the heart of the LDS effort always fail in the light of studied fact. "Oh but you won't find the word "Trinity" in the Bible"
Yeah, you won't find the words Automobile or Dinosaurs either...
The following will be 'a way' to understand the notion of the trinitarian nature of the Deity, not a strictly Biblical explanation, but one which is applicable to the teaching of the Bible. Here goes:
God The Father Almighty is greater than His creation, thus greater than dimension time and dimension space, thus we may think of The Father Almighty as beyond time and space but not prevented from touching and indeed penetrating His creation.
The universe of space and time is likened to a bubble: what is inside the bubble is in time and space. But the nature of what is inside the bubble is only partially understood in modern Physics.
The Bible relates scenes which defy our simplistic notions, but let us make the statement that God The Father Almighty is as comfortable outside the bubble of our spacetime as He is inside the bubble.
Modern Physics has discovered that the balance of forces and tensions sustaining the universe necessary for human life to arise within the universe is extremely delicate, on the order of a mathematical improbability, represented as a 'one in less than' fraction so tiny that a one over a one followed by more than one-hundred zeros [1/1x10100] defines the probability that the whole thing remains in balance! Such a delicate balancing act is but one of the continuing 'works' of the Holy Spirit of God. It is by the Spirit of God, The Word, that the universe came into existence and it is said in the Bible that by His Spirit the whole is maintained.
But the Bible also states that The Word was with God in the beginning and was God. In John's gospel we find that Jesus is The Word made flesh Who dwelt among us. So, inside the bubble Created by The Father Almighty, sustained by God The Holy Spirit, is the Word, God made flesh Who dwelt among us. The Creator does not stop being greater than His creation bubble, nor does His Spirit cease to sustain it all in balance, when Jesus comes in the flesh to dwell among us.
When one reads the Tanakh/Old Testament, one finds scenes like the fifth chapter of Daniel where a being is in one spacetime 'where/when' reaching into another 'where/when' to write on the palace party central wall of king Belshazzar. Just the forearm/hand is seen in the where/when of Belshazzar and the party folks, the rest of the being remains in 'another' where/when.
God The Father Almighty created this 'other' where/when, His Holy Spirit maintains its balance and separateness from our where/when, and Jesus has moved in and out of this other where/when: as shown when He resurrected from the tomb without rolling away the stone, just passing out of the tomb where/when, into 'another' where/when; then back into our where/when as He spoke to the women come to the sepulchre; and when He appeared in a locked and shuttered room with the disciples present; or appeared suddenly with the disciples walking on a road and broke bread with them then left our where/when to go to the 'other' where/when.
The trinitarian nature of God is shown in the Bible, even in the Tanakh. Trinity IS the nature of God as we have been given to know. Even in the Old Testament/Tanakh, we do have instruction on the Three nature of God as Creator, Sustainer, and Deliverer. God Is manifested as three yet one, seen identified by the 'work' He is doing/'action' He is taking.
With each manifestation, we are given to realize His presence simultaneously as Creator--because we exist in the realm He created, as Sustainer--because the balance is too delicate to stand alone without His sustaining the separation and interdependence, and as God with us in the person of Jesus our Lord and Savior.