Midrash sa Levitico 12:6: Bereshit Rabbah, Sifra, Midrash Tanchuma & Midrash Tanchuma Buber

Beit Shammai and Beit Hillel, Beit Shammai say: The heavens were created first and the earth was created thereafter. Beit Hillel says: The earth was created first and the heavens thereafter.⁶⁰One verse puts the order as “God created the heavens and the earth” (Genesis 1:1), but another has the opposite: “On the day that the Lord God made earth and the heavens” (Genesis 2:4). Which is the true chronological order? These cite a reason for their position and those cite a reason for their position. According to the opinion of Beit Shammai, who say that the heavens were created first and the earth thereafter, it is analogous to a king who had a throne made, and once that was made he had its footstool made. So, the Holy One blessed be He said: “The heavens are My throne and the earth is My footstool…” (Isaiah 66:1). According to the opinion of Beit Hillel, who say that the earth was created first and the heavens thereafter, it is analogous to a king who built a palace; first he built the lower sections and then he built the upper sections, so, “on the day that the Lord God made earth and the heavens” (Genesis 2:4).⁶¹The earth first, then the heavens. Rabbi Yehuda bar Ilai said: This verse, too, supports Beit Hillel: “You laid the foundations of earth in times past” (Psalms 102:26), and then, “the heavens are the work of Your hands” (Psalms 102:26). Rabbi Ḥanin said: From the same place where Scripture supports Beit Shammai,⁶²"God created the heavens and the earth” (Genesis 1:1). from there, Beit Hillel refute them: “The earth was” (Genesis 1:2) – it already was.
Rabbi Yoḥanan said in the name of the Sages: In terms of Creation, the heavens were first, but in terms of completion, the earth was first. Rabbi Tanḥuma said: I will say the source; in terms of Creation, the heavens were first, as it is stated: “In the beginning, God created [the heavens].” In terms of completion, the earth was first, as it is stated: “On the day that the Lord God made earth and the heavens.”
Rabbi Shimon ben Yoḥai said: I am surprised how it is that the fathers of the world, Beit Shammai and Beit Hillel, disagreed regarding the creation of the heavens and the earth. It is, rather, as I say, that both of them were created [at the same time,] like a stewpot and its lid, as it is stated: “[My hand also laid the foundation of the earth and My right hand measured the heavens]; I appointed them; they arise together” (Isaiah 48:13).
Rabbi Elazar ben Rabbi Shimon said: If it is in accordance with the opinion of my father, why is it that at times the earth is mentioned before the heavens and at times the heavens are mentioned before the earth? Rather, it teaches that both of them are equal in importance to one another.
In every place Abraham is mentioned before Isaac and Jacob, but in one place it says: “I will remember My covenant with Jacob, [and also My covenant with Isaac, and also My covenant with Abraham]” (Leviticus 26:42). This teaches that the three of them are equal in importance to one another.
In every place Moses is mentioned before Aaron, but in one place it says: “It is Aaron and Moses” (Exodus 6:26). This teaches that both of them are equal in importance to one another.
In every place Joshua is mentioned before Caleb, but in one place it says: “Except for Caleb son of Yefuneh the Kenizite and Joshua son of Nun” (Numbers 14:30, Numbers 32:12).⁶³The citation in the Midrash is actually an amalgam of these two verses. This teaches that both of them are equal in importance to one another.
In every place turtledoves are mentioned before young pigeons, but in one place it says: “And a young pigeon or a turtledove as a sin offering” (Leviticus 12:6). This tells you that both of them are equal in importance to one another.
In every place, honor of the father is mentioned before the mother, but in one place it says: “Each of you shall fear his mother and his father” (Leviticus 19:3). This tells you that both of them are equal in importance to one another. However, the Sages said: The father takes precedence over the mother, because both he [a son] and his mother are obligated to honor his father.
In every place the creation of the heavens is mentioned before the earth, but in one place it says: “On the day that the Lord God made earth and the heavens.” This tells you that both of them are equal in importance to one another.

1) (Vayikra 12:6) ("And when the days of her purification are fulfilled (melos), for a son or for a daughter, she shall bring a lamb in its first year for a burnt-offering, and a young pigeon or a turtle-dove for a sin-offering, to the door of the tent of meeting, to the Cohein.") "when they are fulfilled": She does not bring it in the midst of melos; if she does, she has not fulfilled her obligation. I might think that she may not bring it in the midst of melos (for this birth, even) for (the unfulfilled obligations for) previous births; it is, therefore, written "she shall bring." "for a son": she is liable for each son. "for a daughter": she is liable for each daughter. "or for a daughter": to include a woman who miscarried on the eve of the eighty-first day (of melos for a girl) as being liable for an offering, in accordance with the view of Beth Hillel. For Beth Shammai exempt her from an offering (for the miscarriage, even though it took place after melos [the end of the eightieth day]. For since an offering cannot be offered at night, it is considered as if it took place in the midst of melos). Beth Hillel queried Beth Shammai: How is the night preceding the eighty-first day different from the eighty-first day itself? (Furthermore,) if the former is equivalent to the latter for purposes of tumah (i.e., niddah), why should it not be so for purposes of an offering? Beth Shammai responded: No, if this is true of the eighty-first day, it is because she arrived at a time that she could bring an offering (for her first birth). Would you say the same for the night preceding the eighty-first day, when she has not arrived at a time that she can bring an offering? Beth Hillel: But this is refuted by the instance of a woman's miscarrying on the eighty-first day that falls on a Sabbath, in which instance she is liable for an offering even though that day (Sabbath) is not fit for an offering! Beth Shammai: No, for in that instance, even though it is not fit for an individual offering, it is fit for a communal offering, as opposed to the instance of a woman's miscarrying on the night preceding the eighty-first day, the night being fit neither for an individual offering nor for a communal offering.

2) And blood (i.e., your argument from tumah) is no refutation, for if a woman miscarries in the midst of melos, her blood is tamei and yet she is exempt from an offering (so that there is no necessary correction between the two). Beth Hillel said to them: "or for a daughter": to include a woman who miscarried on the eve of the eighty-first day (of melos for a girl) as being liable for an offering.