The world was created in the month of Tishrei, and accordingly Rosh HaShana is on the first of Tishrei. Nevertheless, at the time of the redemption from Egypt, in the month of Nisan, we were commanded to make Nisan the first month. Our calendar is special in that it is connected to the redemption and to the Torah, and not only to Creation and nature.

“This month is for you” (Exodus 12:2): Although it is not in itself fitting that it should be “the beginning of months” [since the world was created in Tishrei], it is fitting for you that it comes first, since you were redeemed in it, and the Torah began for you in it. It is fitting that all of our timekeeping be rooted in the Torah and not the natural order, because we do not operate in accordance with nature, but rather entirely according to reward and punishment. (Rabbeinu Nisim Gerondi, Derashot HaRan 3)