I seriously doubt that! Paul, being a Pharisee, probably memorized the entire book of Isaiah as young child! Including the verse:
Isa 7:14 Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel.
Paul was QUITE aware of the messianic prophecy of the virgin birth and he was CONVINCED that Jesus was the Messiah. Immanuel - God with us.
Paul should have, could have, would have, sure. But none of his letters indicate it. If you are going to hang your hat on sola scriptura, then this peg is missing.
You have a misunderstanding of sola scriptura. Peter doesn't mention the virgin birth in his epistles either, but he believed also that Jesus was the Messiah and, as Paul did, wrote to believers in Christ. The prophecies about the Messiah, over 300 BTW, did not need to be reiterated in every writing did they? I think it sufficient that Paul never disputed Jesus' fulfillment of that prophecy.
Silliness...Or wilfull deception...
Act 20:27 For I have not shunned to declare unto you all the counsel of God.
Paul taught ALL of the scriptures...He didn't omit the Gospels...Paul didn't mention Nehemiah in his epistles...Does that mean Paul didn't believe in Nehemiah??? Silly...