I think she did. But it’s harder to see that because of how the story is translated and changing views on human physiology.
The way modern Bibles tell the story, it starts with “the man” trading a “rib” for a “helper.” Androcentric traditions became encrusted in translation. Instead, the word adam indicates a kind – humankind – not a sex. The word ish indicates a man, and it’s used when the man celebrates the woman. Before that, the adam isn’t called a man.
God forms the human, blows life into its nostrils, then gives instructions on what to eat and not eat. These instructions are for the human alone, but God sees that this loneliness is not good. God promises to make an ally as a partner. In the Hebrew grammar, both the human and the ally are masculine nouns, but that doesn’t prove they’re males. Hebrew tends to use the masculine when sex and gender aren’t in view – or are mixed or can’t be determined. The masculine is the default. At this point, the story doesn’t reveal the sex of the promised ally or the human.
God makes all the animals from the ground and invites the human to meet them. The human names each one, but recognizes that none is a suitable ally. So God casts the human into a deep sleep, then takes one tsela – one side – that will soon be used to build a woman. Dozens of biblical examples show that this Hebrew word means a side and not a rib. After removing one side, God closes up the flesh of the remaining side. This half, now a complete person again, will soon call himself a man. Finally, God builds the half that was taken into a woman.
Forming the woman from living flesh reveals another detail that modern readers easily miss. In ancient Near East worldviews, a person thinks, makes decisions and feels emotion with their guts. Later cultures located a person’s mind in an immaterial soul distinct from their body, but for early audiences of Genesis the mind resides in the physical guts. Since God had removed a full side, the story shows that the woman was made from the human’s guts – from organs that were already functioning. Because the one body became two, the one mind also became two.
The woman’s mind is not a blank slate. She knows how to speak. She heard God’s commands. She’s already met every creature in the garden. She remembers giving each one a name that showed it was not on her level. But now, she looks up to the snake and considers it an ally that can help her on her way. The story depicts her turn from God well before she takes an illicit bite.
The woman relates to the man much like Judah relates to Israel. Similar to how some of Israel split off to become the nation of Judah, God split off a side of Adam to form Eve. These special parts, Judah and Eve, are not less than their counterparts who continue to be known by more common names. And further, the narrative of the solitary Adam forms the first chapter of both Eve and Adam’s life, just as the history of united Israel provides the shared backstory for Judah and Israel.