Holy Trinity
How can 3 distinct persons make up one being?
A: The problem is that you presume that 'being' and 'person' are equivalent, though you don't state it.
To phrase it better parabolically:
How can six squares be a cube?
A square and a cube are not the same thing, yet the cube does not exist separately from the squares.
So how do they differ?
The Father knows stuff that the Son and the Holy Ghost don't, such as the time of His coming.
The Son has a personal will which differs from the Father's. He did not want to die, hence the prayer to remove the cup. However, he submitted his will to that of the Father. This is prefigured by the bruised heel of the seed of the woman and withered thigh of Jacob.
Since the Son leaves the Father and Mother and cleaves to the bride, the separation between Father and Son which occurred at the cross was not fully restored in the resurrection. Though there is a reconciliation, there is something that remains separated. The reconciliation is foreshadowed by the parted water which was restored, but the split rock and the torn veil were not restored. Christ is eternally married to the flesh and to the church.
The Holy Ghost proceeds from the Father and was sent by the Son. The book of Jonah starts out: The Word of God (Christ) came to the dove (the Holy Spirit) ... and tells the Holy Spirit's role in the cross... how he was separated from the Son at the cross, was grieved and took comfort from the Son after the resurrection. Jesus sends him as "another Comforter" because the Son is the first comforter.
The story of the sons of Eli tells us that when anyone repents, the Holy Spirit wields the three prong flesh hook of the law and rips flesh from the side of Christ in His tribulation, whereupon Christ marries the flesh. It is the same picture of Adam's rib where the church comes from the flesh of Jesus while he is dead.
Each of the "squares" or persons is different from each other, yet they are the same "cube".
When we add a fourth dimension to space we get space-time. When we add another dimension to person-hood, we get a description of God.
Is the Holy Trinity mentioned in the Old Testament? The shadows speak more clearly of the Trinity than the literal-historical.
Together Abraham, Isaac, and Jacob represent the Trinity. Abraham is the Father who offered his son. Issac is the son who was offered as a sacrifice. He did not get the blessing to be fruitful. Jacob is the one who was fruitful.
Abraham, his servant and Isaac also represent the Trinty. (The servant gathered the bride).
There is also an undeniable pattern of three represented in the New Testament as "hearing, seeing, and walking". When God spoke to Israel from the mountain they refused to hear. When he showed them the law, they refused to see, and when he lived among them as the pillar, they refused to walk.
He revealed Himself to all men (made Himself manifest) and we refuse to hear. All creation testifies and we refuse to see. God dwells among us and we refuse to walk.
The Father speaks, the Son shows, and the Spirit gives life. This pattern is everywhere in the OT.
We also have the testimonies of the patriarchs (Father) and of Israel (called the son of God) and of the life of Christ (where the Spirit bears testimony of his birth, baptist, etc.)
In Genesis 1, God speaks, The son (firmament, life and light) works, and the Spirit gives life as stuff springs up.
The three friends of Job represent God who is three in heaven. Job represent the one who is three on earth, and they are one, which is why the candle has seven and at the end of Job there were seven burnt offering to reconcile Job and his friends. (And why he cries "I am innocent, why won't you hear my defense?")
Correlating the three women at the well you have Abraham (Father) who chooses the bride for his son, Jacob (Son) who woos, or calls his own bride, and the Holy Spirit who gathers the woman to the church at Sychar.
Moses was God (Father) to Pharaoh, Aaron was his mouthpiece (Son) and Joshua was "filled with the spirit".
(further evidence from Ge 1:1-2)