The New Testament writers had a habit of saying things about the Old Testament that are not in the Old Testament but are in these creative, Jewish writings of the period.
What we might call a fast and loose use of the Old Testament was for Paul and his contemporaries a normal and expected approach to biblical interpretation—creatively connecting the past with the present.
Paul appeals to the Old Testament in order to support what is hardly an obvious notion to Jews at the time: that Jesus, a crucified and risen son of a working-class family, is the long-hoped for Jewish messiah and that Gentiles as Gentiles are full and equal partners along with Jews in this messianic age.
Now, I know you believe, as we all do, that the Bible, being God’s word, is perfectly consistent all the way through, meaning it doesn’t mean one thing in the Old Testament and another thing when you quote it. It goes without saying that you respect the intention of the original author more than anyone, and you’d never mistreat the Bible like that.
Matthew interprets Isaiah creatively, not in keeping with what Isaiah meant. The child’s birth is not miraculous in Isaiah, but the deliverance of Judah from a military coalition is.