How do we know that Christ is the God-Man?

Classical Answer: by His WORDS and ACTIONS

Christ claimed to be the Son of God equal to the Father and this is why he was put to death by the Jews. The Transfigulation is an example of his action during which this claim is confirmed by his heavenly Father.

St. Matthew tells us that Jesus was transfigured before Peter, James and John. His face became as bright as the sun and his clothes as radiant as light. And a bright cloud overshadowed them and out of the cloud a voice was heard saying: "This is my beloved Son on whom my favor rests. Listen to him."

Christ the Priest