"The rabbis tried to reconcile these two stories into one coherent narrative. What happened to the woman created in Genesis 1, such that Adam was alone and in need of a mate in Genesis 2? To answer this question, the Rabbis created the legend of Lilith as the first woman. In this legend, Lilith was Adam's equal, but when he insisted on dominating her, she left him. So God created Eve to be Adam's second mate; created from his body, she was more willing to be submissive to him. Thus, Lilith was the woman mentioned in Genesis 1, and Eve the new woman created in Genesis 2 after Lilith fled." - Jewish Women's Archive
(27) And G-d created adam in G-d's image, in the image of G-d did G-d create him; male and female G-d created them. (28)
G-d blessed them and G-d said to them, “Be fertile and increase, fill the earth and master it; and rule the fish of the sea, the birds of the sky, and all the living things that creep on earth.” (29) G-d said, “See, I give you every seed-bearing plant that is upon all the earth, and every tree that has seed-bearing fruit; they shall be yours for food.
(18) Then the Lord G-d said, “It is not good for the adam to be alone; I will make a fitting helper for him.” (19) And the LORD G-d formed out of the earth all the wild beasts and all the birds of the sky, and brought them to the adam to see what he would call them; and whatever the adam called each living creature, that would be its name. (20) And the adam gave names to all the cattle and to the birds of the sky and to all the wild beasts; but for the adam no fitting helper was found. (21) So the LORD G-d cast a deep sleep upon the adam; and, while he slept, G-d took one of his ribs and closed up the flesh at that spot. (22) And the LORD G-d fashioned the rib that G-d had taken from the adam into a woman; and G-d brought her to the adam. (23) Then the adam said, “This one at last is bone of my bones And flesh of my flesh. This one shall be called Woman, For from Man was she taken.” (24) Hence a man leaves his father and mother and clings to his wife, so that they become one flesh. (25) The two of them were naked, the adam and his wife, yet they felt no shame.
(14) Wildcats shall meet hyenas, Goat-demons shall greet each other; There too the lilith shall repose, and find herself a resting place.
(ד) וַיֹּאמֶר הָאָדָם זֹאת הַפַּעַם (בראשית ב, כג), רַבִּי יְהוּדָה בַּר רַבִּי אָמַר, בַּתְּחִלָּה בְּרָאָהּ לוֹ וְרָאָה אוֹתָהּ מְלֵאָה רִירִין וְדַם, וְהִפְלִיגָהּ מִמֶּנּוּ, וְחָזַר וּבְרָאָהּ לוֹ פַּעַם שְׁנִיָּה, הֲדָא הוּא דִכְתִיב: זֹאת הַפַּעַם, זֹאת הִיא שֶׁל אוֹתוֹ הַפַּעַם, זֹאת הִיא שֶׁעֲתִידָה לְהָקִישׁ עָלַי כְּזוּג, הֵיךְ מָה דְאַתְּ אָמַר (שמות כח, לד): פַעֲמוֹן זָהָב וְרִמּוֹן, זוֹ הִיא שֶׁהָיְתָה מְפַעַמְתַּנִי כָּל הַלַּיְלָה כֻּלָּה.
(4) "And Adam said: this is the time..." Rabbi Yehuda bar Rebbi said: In the beginning G-d created her [Lilith], and [Adam] saw that she was full of secretions and blood and separated her from him; and G-d returned and created her [Eve] a second time. As it says: "this is the time" this is the woman this time. "This is the time" for me the one who will be my partner in the future. As it says: "A golden bell (pa'amon) and a pomegranate" (Exodus 28:34). "This is the time" - this is she [Lilith] that perturbed me all night.
דָּבָר אַחֵר, שֶׁלֹא יִהְיוּ אֻמּוֹת הָעוֹלָם נוֹהֲגִין בְּךָ כְּאַכְזָרִי, לוֹמַר בָּא דּוֹר הַמַּבּוּל וְאִבְּדָן, בָּא דּוֹר הַפְלָגָה וּבָאוּ סְדוֹמִים וּבָאוּ מִצְרִים וְאִבְּדָן, אַף אֵלּוּ שֶׁקְּרָאָן (שמות ד, כב): בְּנִי בְּכוֹרִי, הֲרֵי הוּא מְכַלֶּה אוֹתָן, כַּלִּילִית הַזּוֹ שֶׁאֵינָהּ מוֹצְאָה כְּלוּם וְהִיא הוֹפֶכֶת עַל בָּנֶיהָ,
Another interpretation: "Lest the nations of the world think of You [G-d] as cruel. "That is to say: When the generation of the flood came, G-d destroyed them. And similarly, when the generation of the dispersion came, and when the Sodomites came, and when the Egyptians came, G-d destroyed them. And also in the case of these whom G-d has called (in Exod. 4:22), “My first-born son,” He is destroying (mekhalleh) them! G-d is like that Lilith (keLilit). When she does not find anything else, she turns on children.
When God created the first man Adam alone, God said, "It is not good for man to be alone." [So] God created a woman for him, from the earth like him, and called her Lilith. They [Adam and Lilith] promptly began to argue with each other: She said, "I will not lie below," and he said, "I will not lie below, but above, since you are fit for being below and I for being above." She said to him, "The two of us are equal, since we are both from the earth." And they would not listen to each other. Since Lilith saw [how it was], she uttered God’s ineffable name and flew away into the air. Adam stood in prayer before his Maker and said, "Master of the Universe, the woman you gave me fled from me!"

She did not wander long on the other side before she met the one she had come to find, for Lilith was waiting. At first sight of her, Eve remembered the tales of Adam and was frightened, but Lilith understood and greeted her kindly. “Who are you?” they asked each other, “What is your story?” And they sat and spoke together of the past and then of the future. They talked for many hours, not once, but many times. They taught each other many things, and told each other stories, and laughed together, and cried, over and over, till the bond of sisterhood grew between them.
Meanwhile, back in the garden, Adam was puzzled by Eve's comings and goings, and disturbed by what he sensed to be her new attitude toward him. He talked to God about it, and God, having his own problems with Adam and a somewhat broader perspective, was able to help out a little—but he was confused, too. Something had failed to go according to plan. As in the days of Abraham, he needed counsel from his children. “I am who I am,” thought God, “but I must become who I will become.”
And God and Adam were expectant and afraid the day Eve and Lilith returned to the garden, bursting with possibilities, ready to rebuild it together." - excerpt from "The Coming of Lilith" by Judith Plaskow (1972)
We are androgynous double-faced beings,
one looking forward and one looking back.
Formed in the light of the throne in the sky,
we are never alone and we never die.
Two forms of dust, of the one and the many;
a vapor to moisten them both into clay.
Two hands to form us, to guide us and shape us,
until we are ready to walk away.
We are, we are, we are,
we are, we are, we are.
We are androgynous double-faced beings,
torn from each other and rendered in two.
Two flaming swords guard the garden of Eden,
but I won’t go back there without you.