Hebrews teaches that Melchizedek was in some mysterious way no less than Christ. Now this may seem like a strange argument to us. We might say that just because no genealogy is mentioned for Melchizedek that does not mean hat he had no genealogy. That is because we are twenty-first century Americans. That is not the way the author of GN operates.
Genealogies are a feature of Genesis.
In ancient society, a person's genealogy established what he was. But Melchizedek arrives out of nowhere. And he arrives out of nowhere as a priest. That was the exact reverse of the Aaronic priesthood. The priesthood of Aaron depended entirely upon ancestry.