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Actually, in Genesis 3:15 there’s an indication that a woman having seed was recognized.

This is known as eisegesis. You're reading something (that it was a common understanding of the time that women had eggs, referred to as 'seed') into what was written. Some believe this is a prophecy of Jesus being born of a virgin and bruising the serpent's head, though there are no New Testament references to it except by the faintest allusion in Revelation where the author speaks of the dragon going to war with the remnant of the woman's seed who keep God's commandments. So here the reference isn't to Jesus but to multiple individuals. At any rate, it wasn't a characteristic of the general culture back then or of the Israelite culture in particular to believe that women had "seed," as though they could, independent of a man, give birth to a child. That's what would make that figure of speech both so shocking as well as a possible prophecy of a virgin birth. It was something that was completely outside the commonly understood order of nature, unless it was just a common way of saying, "Serpent, the woman's son (seed, because it's a male) is going to kick your ass."