In the Written Torah, Genesis 6:18 uses the word covenant - in the Bible's original Hebrew, b'rit, or b'ris - for the first time in connection with Noah (No'ach). God - HaShem - promises:
But with you [Noah] I [God] will establish My covenant, and you shall come into the Ark, you, and your sons, and your wife, and your sons' wives with you.
Covenant appears again, for the second time, in the ninth chapter of Genesis, 9:8 - 9:17: God fulfills His promise; He faithfully establishes His covenant just as He said He would. Covenant is used exactly seven times here. This alludes to - it clearly points to - the Seven Commandments, the sheva mitzvot b'nai noach, the universal moral Law (Talmud, Sanhedrin 56a; Mishnah Tosefta, Avoda Zorah 9:4; Talmud, Nedarim 31a; Genesis Rabbah 16:6, 24:5, 34:8; Deuteronomy Rabbah 2:25; Kuzari 3:73).
So, according to the Written Torah, the First Covenant is the Noahide Covenant - the Universal, Noahide, or Rainbow Covenant. It goes all the way back to Adam and Eve, the first truly human beings, the first men of our species, homo sapiens sapiens - the covenant with Noah and his family, ten generations later, is simply its continuation and renewal. Genesis 9:12 - 9:17 explicitly designates the rainbow as its symbol - its sign.
What can we learn from this? Human beings are not just animals on the surface of a planet. As the Torah tells the story, before Noah and his family, mankind's original common ancestors were Adam and Eve. They were the earth's first truly modern men, more capable and elevated than the primitive men and women who preceeded them. (Noah, ten generations later, was their great great great great great great great grandson.) They enjoyed the benefits of knowledge of God's Way. In other words, God didn't just push human beings out into the world with nothing in the way of guidance. Rather, He inscribed His Law - then constituting only six commandments, and myriad ordinances that accompany them - "on their hearts." (See Talmud, above.)
[As the Torah tells the story, Adam and Eve did not eat meat; only in Noah's time did God give man explicit permission to eat meat, subject only to the last of the Universal Commandments, the Law of the Torn Limb. That is, this is the universal moral law, one of the Seven Commandments, directed to how and what people eat and how we treat our fellow creatures.]
Did this arrangement with the first true humans constitute the First Covenant? A covenant can't be implied; there must be clear covenantal language employed to mark the creation of a covenant. We know of none in this connection. However, if it was a covenant, as most commentators believe (See Hosea 6:7 and commentaries, speaking of the Adamic covenant), the covenant between God and Noah and his family simply ratified, strengthened, extended and continued the original Adamic covenant. So even according to this view, the First Covenant is just the Adamic covenant renewed; the Adamic covenant and the Rainbow Covenant together constituting the First Covenant between God and man.
A covenant means a compact or agreement between two or more parties, marked or memorialized by a pledge. A covenant is a contract of a permanent, unconditional character, unless the words of promise involved explicitly state a condition or limitation of some kind.
In Genesis 9, HaShem makes an eternal, unconditional promise to every earthly creature, including mankind and all animals. This is a one-way promise as to the animals, without any condition of reciprocation. But this is not the case regarding His covenant with Noah and the descendants of Noah - that is, with all humanity.
Human beings have free will, intellect, imagination, and the capacity to behave much worse than mere animals. As God has put us at the top of the planetary foodchain, giving us dominion over the Earth and every plant and creature on - or in - it, He requires us to live up to certain standards. Those standards are part of His covenant with us; He has set them out in His covenantal Law, His Way. He requires us to behave ourselves, to conduct ourselves better than mere animals, in accordance with our exalted, uniquely elevated place in His creation. In other words, the First Covenant - this Adamic or Noahide or Universal or Rainbow Covenant - requires us to act like truly human beings.
[More to come]