it was always part of Mathew.

The fun fact is that Mathew insists this is to fulfill a prophecy in Isaiah. (Mat 1:32, referencing Isaiah 7:14)

The Isaiah prophecy is being given to Ahaz as a sign that his enemies will get rekt. The child being mentioned, here, is nothing more than a time-marker. Basically, what it's saying is, that somewhere a young woman will give birth and name the kid Immanuel. By the time that kid has reached the age of majority or whatever, then everything else (enemies being rekt.) will have happened.

There's a few mistakes the author of Mathew is making here. First. The prophecy was given to Ahaz and could not have possibly been about some kid seven centuries later.

Secondly, in the original Hebrew, the word is most certainly "young woman" or "maiden" not "virgin." so the prophecy isn't even saying there'll be a virgin giving birth. Just a woman, and the sole role the kid plays is to identify a period of time. at that time and place, it would have been around fourteen.

The second mistake comes from the author using the Septuagint instead of the original Hebrew texts. for whatever reason the Greeks translated 'maiden' to 'virgin', and quite incorrectly so. Most modern English translations (particularly for Christians,) make the same mistake because it would be awkward otherwise. Suffice it to say that the author of mathew has exactly zero understanding of the old texts- probably because he was a Hellenic Jew, and spoke/read Greek- not Hebrew or Aramaic.

basically all of the messianic prophecies mathew points to beign fullfilled were either not a prophecy originally, or so severly misunderstood that it's incomprehensible to imagine the author did anything other than throw spaghettified shit at the wall to see what stuck.

"Virgin birth" was already a concept with other dieties. Christians just absorbed myths.

Probably sooner than that. The "Pope" as we know it is an office that evolved later, though the Catholic church claims the line goes back to the Apostle Peter.

The stories in the gospels are a collection of stories that had been circulating orally among the first century Christians, and got written down mostly in the late second half of that century. Mary likely never claimed a virgin birth at all; that was invented by the oral tradition. Pretty much everything about Jesus childhood is made up to push certain religious narratives.

Which itself is sometimes interesting to follow. The whole census story behind Jesus birth, for instance, is almost certainly made up. Why would Rome require everyone to go back to their birth city to register? That's hugely disruptive to everyday life if people have to travel days or weeks just to fill out some paperwork. But why did they stick that in there? One good answer is that the particular group who wrote that section of the gospels--it doesn't appear in all of them--really wanted to connect Jesus to King David and Bethlehem, but everyone knows Jesus is from Nazareth. So they stick this convoluted census story in there to have a reason for Jesus to be born in Bethlehem instead of Nazareth.