Some people do interpret the woman of Rev. 12 as the 'Israel of God' of the New Covenant. Others interpret her as being the nation of Israel of the Old Covenant. Yet others interpret her as being the virgin Mary. And still others say she is the New Testament church which 'births' Christ in the believer. There are probably lots of other permutations on this theme. But this question requires an hermeneutical answer.
To obtain that, all the related scriptures in the Bible would need to be collated and analysed, with the various interpretations compared to that considerable body of scripture. It's considerable because the first mention of "the seed of the woman" is in Genesis 3:15, apparently involving the first woman who was later named Eve - "mother of all living". Then centuries pass with the line of descent traced, involving other women like Sarah, who is an allegory for "Jerusalem above, the mother of us all" (Galatians 4:26), and "We, brethren, as Isaac was, are the children of promise" (vs. 28). The miracle-child, Isaac, was a figure of the birth of the heavenly man child, and of all that shall be born in and of his seed. This allegory is explained in Galatians: Sarah the freewoman answers to Jerusalem above, heavenly Jerusalem.
Yet we find more clues further back in the O.T. Joseph, one of the 12 sons of Jacob (also called Israel) was given a dream from God about the sun, moon and 11 stars bowing down before him (Gen. 37:9-11). Yet Rev. 12 describes the heavenly woman "clothed with the sun, and the moon under her feet, and upon her head a crown of 12 stars"! Here is one hermeneutical comment on that:
"In that dream, Jacob, which is Israel, is depicted as the sun;
Joseph's mother as the moon; his eleven brethren as the eleven stars,
of which he himself therefore - a figure of Christ - was the
twelfth... With the sun the heavenly woman was clothed; the moon was
under her feet; and the twelve stars formed the crown upon her head.
Distinct from her, therefore, but of her glory; if so, Israel was her
heritage. But the heritage of the woman is distinct from that woman.
That with which she was clothed is separate from the woman
distinguished by such clothing. The sun, the moon, and the twelve
stars which formed her heavenly raiment are not to be confused with
the heavenly woman thus arrayed. While vested with these heavenly
bodies, she herself is distinct from them. They speak - from
Joseph's dream - of the glory of Israel. But of what does she
herself speak?" ("The Revelation of Jesus Christ" by John Metcalfe, p278-9)
So far, we have clues that Eve and Sarah and the nation of Israel are part of this symbolic woman, encompassed in this spiritual complexity. In the N.T. this leads to the virgin Mary giving birth to the Son of God, Jesus. Although many things in the Book of the Revelation are obscure, if anything is clear, it is that chapter 12 involves the birth of Jesus! Christ is the seed promised to Eve, for she is mystically designated 'The mother of all living' Gen.3:20. Re. Rev. 12:4-6 when a great red dragon with seven heads, ten horns, and seven crowns appears, desperate to devour her child when born...
"The child is immediately caught up to God and to his throne. Then, no
life of Christ on earth appears in the vision; neither does the cross;
nor the resurrection. In Revelation chapter 12 the ascension is not
viewed as from the earth, beyond death, and after the resurrection: it
is depicted as from the visible heavens... So that those who look for
historical exactitude, or even sequence, in the Book of the
Revelation, err greatly...
Some have conjectured that the heavenly woman is Israel. However,
Israel was not heavenly, but earthly. Again, the signs of Israel - from
Joseph's dream - of the sun, moon, and twelve stars, are not the woman
herself, but that with which she was adorned. But the woman is more
than her vestments. So that she may incorporate much that is of
Israel, but she herself remains a vastly transcendent concept.
Besides, the seed of the woman was the promise given to Eve long ages
before the existence of Israel. And there can be no doubt that the
heavenly woman still answers to Eve in the beginning.
The Roman Catholics refer to the woman in Revelation 12 as Mary...
[But] Mary did not bear the Son in heaven; rather it was in the manger
at Bethlehem. But the heavenly woman in vision bore the man child in
the visible heavens. Mary's child was not immediately caught up to the
throne of God in heaven, but shortly taken down the road to Egypt.
Mary did not flee - after the child was caught up to the heaven of
heavens - into the wilderness, there to exist for the entirety of the
age till the coming again of Christ. But that is exactly what is
foretold of the heavenly woman. Finally, Mary did not live in the
wilderness bearing, generation by generation, till the end of time,
'The remnant of her seed' (vs. 17)." (Ibid pp282-3)
A literal, physical and virgin woman did give birth to the man child, Jesus, but if she be the heavenly woman, then she also gave birth to myriads more - 'the remnant of her seed' whom the dragon then tries to drown. If the Catholic interpretation requires a physical woman on earth at the start, then switches to symbolic and heavenly interpretations for 'the remnant of her seed', that is to violate the principles of consistent, hermeneutical interpretation. Numbers in the Revelation are symbolic, not literal - another trap many fall into is thinking some numbers are literal, but the rest of the sentences containing those numbers are symbolic. However, the author I quote adds:
"Nevertheless it is true that Mary was the visible earthly culmination
of a heavenly series of visionary prophecies spanning the whole of
time and incorporating increasing openings from the beginning of
scripture... In such vast and divine imagery, the visionary heavenly
woman of necessity includes Mary, just as it does Eve, but the graphic
imagery of the mysterious vision vastly transcends the individual.
Others have caught themselves in worse fables... that the woman is the
church... The church bears the man child?... Eph. 5:32. Then, since
Adam preceded Eve, Christ of necessity preceded the church. How then
could she have borne him, when she did not so much as exist until
the ascension? Once more, if the church appears at all in Revelation
Chapter 12, it is as 'the remnant of her' - the heavenly woman's -
'seed'. But if the ecclesia be the remnant of her seed, then she,
the mother of that seed, cannot possibly be the same as that
ecclesia which she bears. (Ibid. p281-2)
The book explains much more until reaching its conclusion on the matter:
"This same Jerusalem above, heavenly Jerusalem, called 'the mother of
us all', agrees with the great sign of the heavenly woman bearing
Christ the firstborn, and in him all the elect seed from before the
foundation of the world... In fine, the great sign of the heavenly
woman in the vision of Revelation chapter 12 depicts her as the symbol
of that reality, that heavenly totality of divine thought, which
brought Christ down from heaven. She is the origin of his coming
forth, the opening of truth which was the cause of his being born as a
man. Out of the womb of ancient, lingering, divine promise, truth, and
purpose, nothing but the coming of Christ yielded fulfilment and
brought consummation to its fulness... The heavenly woman, for a
moment of revelation, stands for ever as the embodiment of a
transcendent vision in the mind of God, which Christ, issuing forth,
brought to pass in himself. In a word, she is the concept that bore
Christ and his seed, called heavenly Jerusalem, and spiritual Zion."
So, my answer to your question is that a sound interpretation of who this symbolic Woman is, requires expanding our thinking to incorporate all that forms the mind and will of God to fulfil his promise in Genesis 3:15. Included in this symbolic Woman are literal women (like Eve, Sarah and Mary), also literal Israel that foreshadowed spiritual Israel (thus incorporating both Old and New Covenants). The heavenly Son and the Holy Spirit are equally involved in the mind and will of God to utterly crush the great red dragon, who is revealed in all his horror at the incarnation, but defeated at a stroke by the man child, the heir apparent, instantly being caught up to God and his throne at the moment of his appearing. This concept of The Woman is vast. We are generally far too narrow-minded (with vested interests in promoting one, small aspect) and miss out on the immensity of the sign that Revelation chapter 12 shows us.