“He is the radiance of the glory of God and the exact imprint of his nature [kai charaktēr tēs hypostaseōs autou] and he upholds the universe by the word of his power. After making purification for sins, he sat down at the right hand of the Majesty on high,” (Heb 1:3 ESV)
The author of Hebrews expands on describing the Son’s radiance of the glory of God by ascribing to the Son, “the exact imprint of [God’s] nature.” The Greek expression used is highly significant: “charaktēr tēs hypostaseōs autou.” This statement about the Son being the exact representation of the essence of God tells us two things about the Son: (1) He is divine, and (2) is distinguished from another person (the Father in this case) because he shares in—represents—the same nature as another person.
For if the Son were the Father, it would be strange, if not illogical, to speak of him as the representation of God’s nature. There are two persons in view here, not one.
Moreover, the last statement in this verse, “he sat down at the right hand of the Majesty on high,” demonstrates two co-existing persons.
Therefore the Son cannot be identified as the Father.