As a native Hebrew speaker, who happened to have read the OT and NT through, I'd like to add something.
The prophecy in Isaiah 53 say "Hineh ha'alma hara ve'yoledet ben": "behold, the young woman will conceive and bear a son". It is often said, correctly, that the word "alma" (lit. "young unmarried woman") does not necessarily mean "virgin". But that isn't nearly the only problem.
From various untranslatable grammatical and contextual reasons in the original Hebrew, it is obvious the writing could only mean "someone who is a young woman now (at the time of the prophecy, ca. 600 BC or so) will in the future have a son, which..." (etc.); much like I could point to a six-year-old and say "she will be a good mother" if I see her taking care of her younger brother.
It does NOT, and COULD NOT, mean that, hundreds of years later, there will exist someone who would still be a virgin (or unmarried, for that matter) when she has a son, any more when I look at a six-year-old and saying, "This six year old will be a good mother", I could possibly mean that, hundreds of years from now, a miraculous child will exist who would be a good mother when she's six years old.
So the whole "does Alma mean virgin, or young unmarried woman?" discussion is besides the point. The whole prophecy could only refer to someone eventually born, in the normal way, to a woman who was a young unmarried woman, or a virgin, ca. 600 BC -- NOT to someone who will give birth, when still a virgin, hundreds of years later.
The whole Isaiah 53 thing is just the usual shoe-horning of vague prophecies into later events.