First of all, no. Almah means simply "young woman." An unmarried, virginal state is implied (of the seven times almah appears in the Tanakh (OT) it is never used of a non-virgin), but not required. In fact, there is no single word in Hebrew that means "virgin" in the modern sense. (No, "betulah" didn't originally mean "virgin" either; the word changed in meaning later.)
By the way, the Greek "parthenos" may not have originally meant "virgo intacta" either; that's why Luke records Mary saying, "I am a parthenos, who has never known a man." The last clause would be utterly superfluous if parthenos always and only meant "virgin" in the modern sense--and the Spirit never wastes words.
Secondly, the DSS don't rescue you there, since they also have "almah" in this passage.
Thirdly, there is not a single Jewish source that I have ever heard of that uses this passage to "prove" that the Messiah would be born out of wedlock. There are passages in the Talmud that accuse Yeshua of being born such, but they don't use Isaiah 7 in reference to Him.
Matthew did not find Isa. 7:14 and say, "Oh look, it says the Messiah would be born of a virgin!" Rather, he said, "Hey, we know that the Messiah was born of a virgin; are there any passages in the Tanakh that refer to this?" From there, he found a string of prophecy that runs from chapter 7 through chapter 12 of Isaiah about the Messiah which says that He would a) be born of an almah, and b) this would be a miraculous sign, and c) this child would be called "God With Us."
There are certainly variants in the Masoretic Text (heck, the text records quite a number of spelling variants in what are known as qere-ketiv notations). There are also a handful of places where these variants impact messianic passages--but not in Isaiah 7.
Shalom
I don’t think we’re disagreeing as much as your tone suggests. You acknowledge, “In fact, there is no single word in Hebrew that means “virgin” in the modern sense.” Yet, “parthenos” is used several times in the New Testament; so when Jesus spoke “virgin,” he was speaking whatever Hebrew word would have connoted “virgin.” And the word which connoted “marriageable” (if not strictly denoting it) was “almah.” So we find a fairly strong suggestion for making the association that “almah” = “parthenos,” in the dialect of Christ.
Yes, “parthenos” did not mean “virgin,” either. Temple “virgins” knew man, but Mary was no “temple virgin.”
I did err on the DSS. They show that the LXX was accurately based on a different set Hebrew scriptures, rather than being, as was believed for 1600 years, strangely inaccurate translations of the same Hebrew scriptures which the MT was based on. But as you correctly note, they did use the word, “Almah.” I think my point still stands, however: Since the LXX is proven not to be an inferior translation, it’s pre-Christian translation of “Virgin” to “Parthenos” established a prophetic precedent that Christ would be born of a virgin; any translation which fails to reflect this is at odds with the meaning of the prophets as known to those with the apostolic authority to write the New Testament.