We were (are?) Bnei No’ach
When we were about to be leaving Egypt, G-d commanded us to set up a new Jewish Calendar with the words, “THIS month (Nissan) shall be for YOU the first of your months; your first of the months of the year.” And sure enough, Nissan is month number one, Iyar is the second month, etc. The implication of this first mitzva to Bnei Yisrael is that we would leave the old calendar reckoning to the rest of the world and we would have a calendar that focused on the Exodus, rather than Creation of the World. This idea is supported (it can be said) from the wording in the opening statement/mitzva of the Aseret HaDibrot, ANOCHI HASHEM ELOKECHA.Who took you out of Egypt..., not Who created the World.

Until the fateful experiences of Y’TZI’AT MITZRAYIM / MATAN TORAH, we were fellow members of the human race, all the descendants of No’ach, but from then on, we are a “nation apart” (in many senses of the term), descendants of Avraham, Yitzchak, and Yaakov, Bnei Yisrael. As opposed to Bnei No’ach.

Yet, it didn’t happen exactly like that. Rosh HaShana 5763 might have been the first (and second) days of the seventh month, but it was also the beginning of the 5763rd year since Creation (let’s not argue about whether we start counting from zero or one). We did not abandon the counting from Creation; we added the Exodus as another “starting point”. We, the Jewish People, are Bnei Adam, descendants of Adam HaRishon and Chava, human beings. And we are different from that, more than that. We are ALSO Bnei Yisrael, Jews.

Being Jewish did not mean resigning from the human race, turning in our Bnei No’ach cards for new identities. It meant being the People from AMONG all other people who accepted G-d’s special challenge to pursue a special relationship with Him and to undertake a quest of Holiness that raises us above the mundane world, while we are still part of it.

Perhaps the Ladder of Yaakov is a good model of this status — the ladder was standing on the ground and its top reached the heavens.

Maybe this is why the Torah starts with a sedra about Adam and the generations that followed from him. And then a sedra about No’ach and the generations that followed from him. And only then are we introduced to Avraham Avinu and Sara Imeinu and the other Avot and Imahot.
The ZICHRONOT bracha of the Rosh HaShana Musaf includes (begins) with No’ach and how G-d “lovingly” remembered him (and family and TEIVA inhabitants).

TZELEM ELOKIM includes our whole species, not just the Jewish People. We need to be connected to the whole world to PROPERLY be “a nation apart”. Being a “mensch” is part of being a Jew.