Isaiah 7:14 Therefore the Lord himself will give you a sign. Behold, the virgin shall conceive and bear a son, and shall call his name Immanuel .
ESV footnote  Immanuel means God is with us
Matthew 1:23 “Behold, the virgin shall conceive and bear a son, and they shall call his name Immanuel” which means, God with us.
The background to the question.
1. Maiden in the ancient world.
For obvious reasons the distinction between “virgin” and “maiden” in the ancient world — particularly in Hebrew — is far less significant than in the modern world. Among Jews, Greeks, and any ancient culture, it was assumed that a “maiden” (an unmarried girl) was a “virgin” (medically) and the two words are frequently interchangeable. This is demonstrated by the Jews who translated the Old Testament (OT) scriptures into Greek: the Septuagint translates the Hebrew for “maiden” (almah) in Isaiah 7:14 into the Greek for “virgin” (parthenos).
But, if this is ignored, there is potentially something in Jewish objections, since the Hebrew text of Isaiah says a “maiden” (Hebrew almah) will be with child, not a “virgin” (Hebrew betulah). However, following on from the historical context in Isaiah 7-8, it is most likely that the child to be born is Hezekiah, and that his mother was indeed both a “maiden” and therefore also a “virgin” when Isaiah made the prophecy. Although Ahaz had already had at least one pagan concubine (since he sacrificed the pagan child to Moloch: 2Kings 16:3), the Isaiah 7-8 prophecies appear to be made at the time of one of Ahaz’s occasional repentances, when Isaiah (or someone else) had brokered a marriage between Ahaz and Abijah, daughter of the High Priest, possibly as a condition of Isaiah and the priests support for Ahaz. The daughter of the High Priest would clearly not only be a “maiden” in name, but also a “virgin” in nature at the time of the betrothal. But Isaiah does not claim that a virgin would conceive since, clearly, Hezekiah’s conception was totally natural.
What is wrong with the Jewish objection, though, is a rather anachronistic way of looking at Matthew’s use of Isaiah 7:14. First, as we’ve noted, the difference between “maiden” and “virgin” in the ancient world was not significant unless demanded by the context.
2. Greek New Testament use of the Greek, not Hebrew, Old Testament
Second, Matthew was only quoting “virgin” (parthenos) from the common Jewish Greek OT (the Septuagint), as used by Diaspora communities and “God fearing” pagan sympathizers with Judaism throughout the Mediterranean. We know this since, if Matthew had not quoted according to the existing version, his argument would have been meaningless, and also because of the well-documented (if from a Jewish perspective quite understandable) campaign to revise all Jewish versions of Isaiah from “virgin” (parthenos, in Septuagint) to “maiden” (neanis, in OT of Symmachus, etc.) during the 2ndC. CE as Christianity made increasing converts among Jews.
3. The earlier Immanuel as a foreshadow
Third, there’s an anachronism in judging Matthew’s use of the Isaiah text through modern rabbinical eyes. Matthew, like Paul and the other NT writers, lived in and preached to the Hellenistic Jewish world prior to the dual cataclysms of the Fall of Jerusalem (70 CE) and The Bar Kokhba revolt (132–136 CE) . Objections to Matthew’s way of using the OT Immanuel prophecy about Hezekiah in application to Jesus are missing the point about how the NT writers, and many other Jews in this period, viewed the Old Testament in terms of typology, or (in the language of Col.2:17, Heb. 8:5 etc.) “fore-shadows” of things to come. Matthew’s use of the Isaiah Immanuel prophecy here is far less controversial than Paul’s analogy of Sarah and Hagar in Gal.4:22, or of many of the types in Philo of Alexandria or the Talmuds. Together with this concept of type and foreshadow comes the related (and well demonstrated) concept of dual-fulfillment in Old Testament prophecies. The fact that Matthew’s audience around the Mediterranean found this kind of argument convincing is proven by the fact that Matthew’s worked well enough to provoke wholesale editing of later Jewish copies of Greek Isaiah.
4. Adoption into Solomon’s line
Fourth, the objection is also forgetting that Matthew has a second purpose in using the Immanuel prophecy beyond simply demonstrating a foreshadow of the virgin birth, which relates to the legitimacy of Christ’s standing in the Solomonic line. Matthew has just at length listed Christ’s (in fact his adoptive father Joseph’s) legal descent via Solomon, and via Hezekiah in Matt.1:10, so Matthew’s use of the Is.7:14 prophecy here is no coincidence — it is part of Matthew’s argument presenting Christ as rightful heir in the legal and royal line from Solomon, which Matthew demonstrates by showing that Christ legally was, by virtue of being born in the house of Joseph. It was important for Matthew to do this (for his Jewish audience) as the physical descent from the minor Davidic line through Mary would be of little value to Jewish readers. The minor royal line is given in the Luke genealogy — written for a Greek audience — where we see that his mother Mary was descended from Solomon’s brother Nathan (2 Sam.5:14, Luke 3:31). Admittedly, Matthew could, to make this point about Jesus being in the Solomonic line, legally, just as easily have written “maiden” (Greek neanis) not “virgin” (Greek parthenos), but given what was said in the first three points above, particularly the second, why should he have? The original “virgin shall conceive” was itself a God-arranged intervention in the line of the Jewish kings, even though the marriage of Ahaz with Abi (2 Kings 18:2) was only providential rather than miraculous.