It's a New Year - says who?

(1) They are four New Year days:

1. On the first of Nisan is the New Year for kings; it is from this date that the years of a king’s rule are counted. And it is also the New Year for the order of the Festivals, as it determines which is considered the first Festival of the year and which the last.
2. On the first of Elul is the New Year for animal tithes; all the animals born prior to that date belong to the previous tithe year and are tithed as a single unit, whereas those born after that date belong to the next tithe year. Rabbi Elazar and Rabbi Shimon say: The New Year for animal tithes is on the first of Tishrei.
3. On the first of Tishrei is the New Year for counting years, as will be explained in the Gemara; for calculating Sabbatical Years and Jubilee Years, i.e., from the first of Tishrei there is a biblical prohibition to work the land during these years; for planting, for determining the years of orla, the three-year period from when a tree has been planted during which time its fruit is forbidden; and for tithing vegetables, as vegetables picked prior to that date cannot be tithed together with vegetables picked after that date.
4. On the first of Shevat is the New Year for the tree; the fruit of a tree that was formed prior to that date belong to the previous tithe year and cannot be tithed together with fruit that was formed after that date; this ruling is in accordance with the statement of Beit Shammai. But Beit Hillel say: The New Year for trees is on the fifteenth of Shevat.

(19) I call heaven and earth to witness against you this day: I have put before you life and death, blessing and curse. Choose life—so you and your offspring would live—

The Gemara explains these matters in detail: It is taught in a baraita that Rabbi Eliezer says: From where is it derived that the world was created in the month of Tishrei? As it is stated: “And God said: Let the earth bring forth grass, herb yielding seed, and fruit tree yielding fruit after its kind” (Genesis 1:11). Which is the month in which the earth brings forth grass and the trees are full of ripe fruit? You must say that this is Tishrei. And a further proof that the world was created in Tishrei is that when the world was first created, it needed rain so that the plants would grow, and the period beginning with Tishrei is a time of rain, and rain fell and the plants grew, as it is stated: “But there went up a mist from the earth, and watered the whole face of the ground” (Genesis 2:6).

Rabbi Yehoshua says: From where is it derived that the world was created in the month of Nisan? As it is stated: “And the earth brought forth grass, herb yielding seed after its kind, and tree yielding fruit” (Genesis 1:12). Which is the month in which the earth is full of grass and the trees begin to bring forth fruit? You must say that this is Nisan. And further proof that the world was created in Nisan is that when the world was first created, the animals had to breed in order to fill the world, and the period beginning with Nisan is a time when cattle, and beasts, and birds mate with one another, as it is stated: “The flocks are clothed in the meadows, and the valleys are wrapped in grain; they shout for joy, they also sing” (Psalms 65:14).