Jesus explicitly mentions all three persons in HIs instruction to His disciples in Matthew 28:19. "Go therefore and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit." The baptism of Jesus. We can see three distinct persons - The Father speaks from heaven, The Son (Jesus) is baptized in the water, and The Holy Spirit descends like a dove. Matthew 3:16,17. "And when Jesus was baptized, immediately he went up from the water, and behold, the heavens were opened to him, and he saw the Spirit of God descending like a dove and coming to rest on him; and behold, a voice from heaven said, 'This is my beloved Son, with whom I am well please." And many other verses. I asked ChatGPT to help me organize and express my thoughts about this using the mathematical operations: It's hard to grasp the Trinity because, when we see three distinct persons, our minds instinctively think of addition—1 + 1 + 1 equals 3, not 1. But if we change the relationship between the numbers to multiplication—1 × 1 × 1—the concept of the Trinity starts to make more sense. Instead of adding separate parts, multiplying 1 by 1 by 1 still gives us 1. This reflects how the Father, Son, and Holy Spirit are distinct persons, but perfectly united in essence. They don't "add up" to something more than one God; rather, they are each fully and equally God, united in their divine nature. While the Trinity remains a mystery, this relationship between the numbers helps us see that the three persons are not separate gods, but one God in perfect unity.

God is not a person. God is a Being.

Within the One Being of God subsist the three persons of the Father, the Son, and the Holy Spirit.

Together, these three make up the One Being of God.

When Jesus was baptised in the River Jordan, all three were present: the Father whose voice was heard from heaven, the Son who was being baptised, and the Holy Spirit who appeared in the form of a dove.

That is why, when the Son died, the Father and the Holy Spirit did not also die. The Being of God was not killed when the Son was killed because the Son is not the Father, the Father is not the Son, and the Holy Spirit is neither Father nor Son.

There has only ever been the One Being of God and there will only ever be the One Being of God.

Expressions such as "person", "Father" and "Son" are used to help us grasp the concept of a complex creator God, although it must be noted that the pre-mortal Jesus was never created, but was active in creation, along with the Holy Spirit.

The best Bible verses to explain this are in John 1:1-5 and 14:

In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of men. The light shines in the darkness, but the darkness has not understood it... The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the One and Only, who came from the Father, full of grace and truth."

Jesus is the Word. Jesus came to earth to be born of a woman. Jesus was God with us, back then. The Son laid down his life then took it up again and has returned to heaven, from whence he first came.

Edit: To Subsist, within the context of the Being of God, is To Exist, To Be.

Response to additional question: 2 Corinthians 6:18 must be read within the context of the previous verses about Christians not being yoked with unbelievers. They are being told to have nothing to do with pagans and idolatry. Verse 18 is a quote from 2 Samuel 7:14 where God, through the prophet Samuel, makes promises to David regarding his kingdom. God says “I will be his father and he shall be my son. When he does wrong I shall punish him... But my love will never be taken away from him as I took it away from Saul.” David was not God’s literal son. This is the explanation given in the NIV Study Bible notes:

This familial language expresses the special relationship God promises to maintain with David’s descendants... It marks him as the one God has chosen and enthroned to rule in his name as the official representative of God’s rule over his people. ”

The Christians in Corinth are being reminded of their special relationship with God. Verse 16 explains: “I will live with them and walk among them, and I will be their God, and they will be my people.”

Romans 8:14 says that those who are led by the Spirit of God are sons of God. In other words, all who have entered into the new covenant Christ Jesus established are adopted into God’s family. It’s a spiritual relationship. Ephesians 1:5 explains: “In love he predestined us to be adopted as his sons through Jesus Christ.”

There is only one Son of God, and that is Jesus, who brought with him his divine nature which was added to his human nature. Those who belong to Christ are adopted into God’s family as sons and daughters, but not physically. 2 Corinthians 6:18 is about our spiritual relationship with God.