Rosh Hashanah is not a biblical holiday, although it replaced a biblical one. It is notably different from the holiday it replaced. The biblical holiday, Yom Teruah, had a totally different purpose than Rosh Hashanah, which focuses on the onset of a new year, repentance, and commitment to live the next year properly. Yom Teruah concentrated on months and the number seven.
The only mention of Rosh Hashanah, New Year, in the Bible is in the writing of the sixth century BCE prophet Ezekiel in 40:1. However, as indicated in Olam Hatanach, Divrei Hayamim, Yechezkeil, page 203, Ezekiel was not talking about the first day of the seventh month, later called Tishrei, the date of the current holiday of Rosh Hashanah, Ezekiel was speaking about the first day of the first month later called Nisan. (The names currently assigned to the Jewish months were assigned in the sixth century BCE during the Babylonian exile.)
According to the Torah, in Exodus 12:2, and as recognized by Ezekiel, the beginning of the year is the month later called Nisan. This is the month in which the Israelites who were freed from Egyptian slavery became a nation. The new year is celebrated by Passover and Hag Hamatzot, on the 14th for one day and 15th of the first month for seven days, as does nature, in the spring. It was only during the Babylonian exile of 586 BCE that the Judeans accepted the Babylonian concept that the year begins in the fall, and the first day of the seventh month begins the new year.
While there is no need to connect the new year with the date of creation, the Judeans began to believe that the world was created on the first day of Tishrei. The Bible does not state the date when the world was created. In fact, if the six day events of creation are taken as six periods of time as indicated in the Babylonian Talmud, Ketubot 57b, which states yamim (days) can mean years, we can understand the Bible saying that creation was a long process with distinct events happening at different times, so there is no single day of creation. The Talmudic sages knew that we cannot pinpoint a day of creation; they even argued homiletically, and only homiletically, about whether the world was created in Nisan or Tishrei in the Babylonian Talmud, Chagigah 12a, Rosh Hashana 8a, 10b-11a, 27a, Avodah Zarah 8a.
As indicated in Leviticus 23:23-25; Numbers 29:1-6, the parent holy day that gave birth to Rosh Hashanah, as I previously noted, was Yom Teruah, also called Yom Zichron Teruah, the day of blowing the horn and the day of memorial proclaimed with the blowing of the horn.
On the first day of the seventh month around the fifth century BCE, Ezra the Scribe gathered the people together and read the Torah, or some of it, to them. According to Nehemiah 8:10, he said to them: “Go your way, eat rich viands, drink the sweet beverages, and send portions to him who has none prepared: for this day is holy to our Lord; do not be sad; for joy in the Lord is your refuge.” Ezra’s joyous description of how the Judeans should celebrate the first day of Tishrei is in no way similar to the way Rosh Hashanah is celebrated today, nor is it similar to the biblical Yom Teruah.
Leviticus 23:25 describes the elements of Yom Teruah. It “shall be a solemn rest to you, a memorial proclaimed with the blowing of horns, a holy convocation. You must do no kind of servile work; and you must bring an offering made by fire to the Lord.” Numbers 29:1–6 supplements this requirement by describing the sacrifices.
Apparently, this day was chosen as a holiday which should be proclaimed to the people by blowing horns because of the number seven. Seven was an important, even magical number, among the pagans. They saw the number everywhere – such as the body parts, two legs, two arms, two parts of the torso, and the head; and they saw seven heavenly bodies among the stars.
The Jews also considered seven important because it reminded them of the existence of God, who created the world in six days, rested on the seventh and gave them laws. Among many other uses of seven, they celebrated the Sabbath on the seventh day and Chag Hamatzot and Sukkot for a week of seven days, marked seven weeks by counting them between Chag Hamatzot and Shavuot, celebrated seven years with a Shemitah Year, and seven Shemitahs with the Jubilee year. They celebrated the first day of the seventh month as another reminder of the significance of seven by adding months to its use in days, weeks, years, and Shemitahs.
Thus it is clear that the invention of Rosh Hashanah and all of its practices, including the idea that this is a day when Jews should repent was instituted after the period of Ezra the Scribe, after the promulgation of the Torah, and after around 500 BCE. Yet it should be observed as tradition commands.