Checking the Strong's Concordance, it is absolutely clear that the word "wife" is always from ISHSHAH in these passages, Strong's number 802, and that same word is also often translated "woman". Therefore the distinction between "wife" and "woman" belongs solely to the translators, and has no connotation whatsoever in relation to the sexual consummation of any husband/wife relationship between Adam and Eve, where it appears in Genesis chapter 2.
Scriptural Proof that Eve was a virgin when the serpent seduced her:
At 4 Maccabees 18:7-8, we find a woman who is obviously being compared to Eve:
4 Maccabees 18:7-8: wrote:“7 And the righteous mother of the seven children spake also as follows to her offspring: I was a pure virgin, and went not beyond my father’s house; but I took care of the built-up rib. 8 No destroyer of the desert, [or] ravisher of the plain, injured me; nor did the destructive, deceitful, snake, make spoil of my chaste virginity; and I remained with my husband during the period of my prime.”
At 2 Corinthians 11:2-3: "Paul compares Eve to a virgin - the allegory must work both ways if he is comparing a "virgin" assembly to Eve:
2 Corinthians 11:2-3: wrote:2 For I admire you with zeal of Yahweh; for I have joined you to one Husband, to present a chaste virgin to Christ. 3 But I fear lest in any way, as the serpent had thoroughly beguiled Eve in his villainy, your thoughts would be corrupted from that sincerity and that purity which is with the Anointed.
