The 4 New Years and Nisan vs Tishrei

(1) The four new years are: On the first of Nisan, the new year for the kings and for the festivals; On the first of Elul, the new year for the tithing of animals; Rabbi Eliezer and Rabbi Shimon say, in the first of Tishrei. On the first of Tishrei, the new year for years, for the Sabbatical years and for the Jubilee years and for the planting and for the vegetables. On the first of Shevat, the new year for the trees, these are the words of the House of Shammai; The House of Hillel says, on the fifteenth thereof.

(1) And the LORD spoke unto Moses and Aaron in the land of Egypt, saying: (2) ’This month shall be unto you the beginning of months; it shall be the first month of the year to you.

It was taught that Rabbi Eliezer said: "In Tishrei the world was created. In Tishrei the forefathers were born. In Tishrei the forefathers died. During Passover Yitzchak was born. During Rosh Hashanah Sarah, Rachel, and Hannah were remembered. During Rosh Hashanah Joseph left the dungeon."

on Rosh Hashanah the bondage of our ancestors in Egypt ceased; in Nisan they were redeemed and in Nisan they will be redeemed in the time to come.

R. Joshua says: In Nisan the world was created; in Nisan the Patriarchs were born; in Nisan the Patriarchs died; on Passover Isaac was born; on Rosh Hashanah Sarah, Rachel and Hannah were visited; on Rosh Hashanah Joseph went forth from prison; on Rosh Hashanah the bondage of our ancestors ceased in Egypt; and in Nisan they will be redeemed in time to come.

It has been taught: ‘R. Eliezer says: Whence
do we know that the world was created in
Tishri? Because it says, And God said, Let the earth put forth grass, herb yielding seed, and fruit-tree. Which is the month in which the earth puts forth grass and the trees are full of fruit? You must say that this is Tishri. That time was the season of rainfall, and the rain came down and the plants sprouted, as it says, And a mist went up from the earth.

R. Joshua says: Whence do we know that the world was created in Nisan? Because it says, And the earth brought forth grass, herb yielding seed after its kind, and tree bearing fruit. Which is the month in which the earth is full of grass and trees [begin to] produce fruit? You must say that this is Nisan. That time was the period when cattle, beasts and fowls copulate with one another, as it says, The rains have mounted the sheep, etc.