‘Without father, without mother.’ Literally? No, not literally.
Some people say that Melchisedec must have been a pre-incarnate appearance of Christ, and that is often quite strongly argued, but that cannot be correct, because Melchisedec offered sacrifices and he functioned as a priest and the Scripture tells us quite plainly, twice in Hebrews alone, that Christ offered himself as a sacrifice once. So he could not have been pre-incarnate in Melchisedec, because Melchisedec functions as a priest and offers up other sacrifices.
Other people say that when Christ came in Old Testament times as a theophany, a pre-incarnate appearance, he came as an angel, but that cannot be right because this very Scripture says that every priest is taken from among men. Valid priests were human beings and they were not embodied angels or something of that kind. They had to be men, and one great type of Christ was Melchisedec, a real man, and a man who became a priest, but he was not a theophany.