Melchizedek is what God the Son is called when He is here, not in the flesh as Jesus Christ, but in a physical spiritual form. In Hebrew, Melchizedek means King of Righteousness.
God the Son has always existed as part of the Godhead (Trinity) (Isa 9:6, Joh 1:1-2) and is the part of the Godhead that is the creative force of our universe (Joh, 1:3, 10, Eph 3:9-12). Also, this is the part of God that interacts with us on a level we are able to understand while we are under the restrictions of the flesh body and mind.
We see Melchizedek throughout the Old Testament whenever God is in a human-like, physical form (Gen 32:24-29, Eze 1, Dan 3:23-25, etc), and we see Him by the name Melchizedek when He is interacting with Abraham in Genesis 14:18-20, where He is called Melchizedek, King of Salem (or King of Righteousness, King of Peace, Heb 7:2). Abraham knew who Melchizedek was, which is why he even brought Him his tithes (Gen 14:20, Heb 7:2). In this chapter, He is in fact even called priest of the Most High God (Gen 14:18, Heb 7:1), a foreshadowing of the fact that Jesus Christ was made our High Priest of God (Psa 110:4-7, Heb 5:6-11, 6:20, 7:17, 21, 8:1-2, 9:11-12).
In Hebrews 7 we are given much more detail on the identity of Melchizedek as the Son of God. In that chapter we are told that He had no mother or father (remember this is God the Son before He came as Jesus Christ in the flesh) and had no children, was not born and did not die, and was made as the Son of God, meaning He had the characteristics of the Son of God (because He was the Son of God).
He was the first to receive tithes (Gen 14:20, Heb 7:4-8), and after His example all the Levite priests would take tithes as well. They would follow this model because He is the model God set for His office of priesthood (Heb 7:5-11). Likewise, we are told that when the Son of God came to us in the flesh as Jesus, His role as High Priest was modeled after Melchizedek (Psa 110:4-7, Heb 5:6-11, 6:20, 7:17, 21, 8:1-2, 9:11-12).
Don’t read over the fact that the entire Godhead has always been with us in one form or another, as each of these parts of God is vital to make up God in His entirety. This is the nature of God.