God revealed himself to Moses as "I am" in Exodus. Jesus revealed himself to his disciples as the "Son of Man" and "Son of God", as worthy of worship and equality with God, often (as in John's gospel) by using "I am" statements: "I am the bread of life", "I am the resurrection and the life", "I am the way, the truth and the light". The Holy Spirit was revealed by Jesus and through its (His?) actions and through the knowledge imparted to the writers of scripture. As Jesus said when talking to Nicodemus in John 3:
5 Jesus answered, “Very truly I tell you, no one can enter the kingdom
of God unless they are born of water and the Spirit. 6 Flesh gives
birth to flesh, but the Spirit[b] gives birth to spirit. 7 You should
not be surprised at my saying, ‘You[c] must be born again.’ 8 The wind
blows wherever it pleases. You hear its sound, but you cannot tell
where it comes from or where it is going. So it is with everyone born
of the Spirit.”
The working of the Spirit is a mystery. In Colossians 1:27:
To them God has chosen to make known among the Gentiles the glorious
riches of this mystery, which is Christ in you, the hope of glory.
I will not argue the "whether" of the trinity, but the "how". The Bible never answers the "how" question. God just is and always has been. He is as he is and not some other God. There is no cause for him, no "how" that can be given.