The Trinity is logical in the right light.
This example doesn't fit: "Yesterday I was with Chuck, I am Chuck" - Big problem.
The right example would be: "Yesterday I was with human, I am human." - No problem here!
Same with the Word: It was with God (the father) and is God (the son). The father was already before time started, so even this works. Maybe the beginning started with the son and then they created everything ...
Even today: When people say God then they usually mean the father, otherwise they say Jesus or Holy Spirit.
But since I am born of a human, I am human. Jesus was born of God, so he is God.
Still not everything is understandable for a human mind - but this one is simple.
Same with being one: John 10:30 "I and the Father are one.”
We are all not the same, but we should be one, when others see us.