I don’t know if you have seen the video I linked, where bible scholar John Huddlestun is interviewed by Richard Dawkins, but in that interview Huddlestun says it’s a well known fact that from early Greco-Roman times/culture, anyone who was important was almost always said to have a god as his father but to be born of a human mother. There’s a relevant quote and a link to the video below, and the most directly relevant statements appear from about 25min. 45sec. (the whole video is of course directly relevant in the overall context of the reliability of the OT, NT and Jesus) -
John Huddlestun interview
https://www.youtube.com/watch?v=21NoQuKTB8Q
“ The idea that your father was a god and your mother a human woman was extremely common in the Greco-Roman period. Anyone who was important at all, whether an Emperor, or Philosopher, or Athlete. If you were anyone important then you would of course have been born of a god and your mother would have been a woman. This was extremely common. The surprising thing would have been if a Gospel writer chose NOT to say that Jesus was born of God with a woman. “
If that is correct, then obviously we cannot use the statement in Galatians where Paul says of “God’s Son”, that he was “born of a woman”, to mean that Paul knew such a thing to be literally true. In that Greco-Roman tradition/belief, a statement like that just means that Paul, or more accurately his anonymous copyist author circa 200AD, simply follows the common tradition of the time and assumes that since this was actually “God’s Son” then he must automatically be born of a woman but with God himself as the father.
As Huddlestun (who does believe in a HJ) says -
“the surprise would have been if any Gospel writer chose NOT to say that Jesus was born of God with a woman. “
It does not mean that Paul or any gospel writer had the faintest idea who Jesus was or who his mother was really supposed to be. And afaik, certainly Paul at least, does not try to name the “mother”.
It might be a different matter if Paul had named the mother and given some actual details of Jesus or his mother and brothers/family that could have been conceivably verified in any reliable way. But of course he did not.
As almost all commentators have pointed out, whether pro or anti HJ, the conspicuous thing about Paul’s letters is that he really knows virtually nothing about any real living Jesus - practically everything that Paul says about his belief in Jesus is theological and not realistic … in fact, perhaps everything he says about his messiah belief is theological rather than ever factual or earthly.
That really only leaves us with the gospels. But as Huddlestun remarks in that video,
g-Mathew is constantly using what bible scholars and historians call “Citation Fulfilment Formulae”. That is; the author of g-Mathew obtained his stories of Jesus by simply searching the words of the OT for any passage which he decided could be applied to his expectation of Jesus. As Huddlestun says (I paraphrase from memory, but check the video) “it did not matter that the actual passage in the OT was clearly not about Jesus but about some other figure or event, g-Mathew simply decided to reproduce or interpret that as if it was about Jesus. And he did that not just with actual prophecies, but with any other parts of the OT that he wished to use”.
In respect of which, afaik everyone agrees that g-Mathew is in fact just an expanded version of g-Mark. That is; g-Mark was also doing that exact same thing, i.e. looking in the OT for any passage that he wished to interpret as an act of Jesus. As I have said here several times; Randel Helms wrote a complete book showing how, why, and where the gospel writers took their Jesus stories from the OT (Randel Helms, Gospel Fictions).
If as all NT scholars seem to agree, Paul’s Letters pre-date the gospels and are the earliest known mention of Jesus, then it’s obvious that later gospel writers producing g-Mark and g-Mathew etc., may have got that idea of searching the OT for Jesus stories, from what had already been written as Paul’s letters. Where the letters repeatedly stress that Paul obtained all his knowledge of Jesus “from no man”, “not of human origin”, “I was not told it by anyone”, ”nor was I taught it by anyone”, but what he preached as his gospel of Jesus, which was “we preach Christ risen”, was known to Paul by “revelation from the Lord himself” and always “according to scripture” through that “which is written” etc.
If the gospel writers knew that Paul had said the belief in Jesus was according to scripture, and because “it is written”, then it is obvious that might have been the reason they scoured the OT for whatever passages they wanted to apply to what were clearly invented Jesus stories.
Finally on the issue of “God’s Son” being “born of a woman” - in Colossians 1:15 Paul says of the “Son” that he was "the firstborn of all creation" and he was “before all things“ etc ., see the quotes below. That is not really compatible with this same “Son“ being born of a normal living woman close to Paul’s own time.
Colossians 1:15
15 who is the image of the invisible God, the firstborn of all creation;
16 for in him were all things created, in the heavens and upon the earth, things visible and things invisible, whether thrones or dominions or principalities or powers; all things have been created through him, and unto him;
17 and he is before all things, and in him all things consist.
18 And he is the head of the body, the church: who is the beginning, the firstborn from the dead; that in all things he might have the preeminence.
19 For it was the good pleasure [of the Father] that in him should all the fulness dwell;
20 and through him to reconcile all things unto himself, having made peace through the blood of his cross; through him, [I say], whether things upon the earth, or things in the heavens.