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.
My understanding of sola scriptura is that if it is not stated or can be derived from scripture, it does not stand. Paul never stated anything about the virgin birth, so you cannot state that he believed in it. What Messiah did Paul believe in? Chapter and verse please? What is the definition of this Messiah? Was it God? Or was it a super David, a great warrior King of Men, a descendant of David, also a Son of God, who would liberate the Jews from the Romans? Chapter and verse please.