Your question qualified based on your comments
“But did that ‘man’ only come into existence at the conception?”
If you are asking about Jesus’ human body, or biological machine that houses the soul and spirit then yes, that was the first time Jesus had a human body.
Quoting the OT
“Consequently, when Christ came into the world, he said, "Sacrifices ...
The doctrine of the Trinity is only about the nature of the divinity of Jesus, whether it's less than or equal to God the Father. So you are right that the Son is eternal like God the Father. The council of Nicaea went even further into defining that there is no time when God the Father existed but Jesus did not.
The human nature of Jesus, on the other ...