You are using the word 'God', in your explanation, where you should be using the word or name 'Father'.
Because God can refer to the Father, or Jesus, or both, at the same time. If you are using all three names, then 'God', has a different meaning, from just the Father...it doesn't mean, just the father, there.
Father & Son are different, however they are both God.
I tried using creator, savior, and spirit. It will relieve the issue of whose god, yaweh, and father.
The creator isnt the savior nor spirit. All three are not the same people. Their roles/activities/persona are extremely different. What makes the trinity is not their same nature (being, human, spirit); they have not. Itd creator, savior, and spirit relationship to each other.
The creator sent the savior. From the savior after his crucifiction came the spirit. The spirit came into those who wished to be born again. As a result, they became crucified in the saviors passion. They looked to him as lord (an authority) because the savior is the way to the creator. Without the savior, there is no union with the creator (christianity).
Trinity means relationship between three things/ideas etc into one unit. They are not each other but one unit together.
The creator, savior, and spirit is those "persons" (not human beings) that make up that unit. That is why its called a trinity. The bible sets it up that way even though it doesnt use the english word for it.
You would need to prove from scripture that
1. There is no relationship between creator, savior, and spirit
2. They are the same in nature and function (meaning no trinity)
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Edit) You'd also have to find in scripture were the savior says he Is, not with, the creator. You also have to show a creator, if a savior, can be born of a human without being a human (not the creator) himself.
Then you have to explain if the creator is the savior, who is the incarnation when their natures are the same