In the pre-flood world, men lived 500-900 years. By the time of Abraham, the time was down to 120-175 years. Yet, if we look at the timeline of everything, Shem could've been alive during the time of Abraham.
Also, his kingdom having "no beginning", ie, he was the last living pre-flood person in the world, so he would've been from a time few could understand.
“The LORD has sworn, and will not repent, You are a priest for ever after the order of Melchizedek.” Psalm 110:4.
Read Hebrews 7:1-17 which shows how Melchizedek was the pre-incarnate Christ whose eternal ministry is in Heaven as our high Priest.
Really cool stuff.
To me, Hebrews' text argues plainly against the pre-incarnation theory, speaking clearly in symbolic and referential terms. I think Melchizidek was his real name and true identity--but suit yourself.