Celebrating Rosh Hashana and the Shofar on the First Day of the Seventh Month
Question
The Tanach mentions that the first (day) of the seventh month (Tishrei) shall be for us a solemn rest and a remembrance of blasts, a sacred occasion/convocation; no work shall be done, it shall be a day of blasting for us. See Leviticus 23:24 and Numbers 29:1.
I would like to know how it was determined or concluded that this day of Teruah is the first, head or start of a annual cycle or year, i.e. is named to be a Rosh HaShanah?
And secondly, what are the blasts a reminder of, what is commemorated at the commemoration when the blasts sound on this specific day?
I know the blasts are often interpreted as the sound of the shofar or silver trumpets; but Teruah is also used to describe people shouting in unison or to describe a joyous sound of happiness and celebration. And in Nehemiah 8:2 and 3 we read about the first of the seventh month as a day on which people were attentive to the scroll of the Torah. Looking at a possible explanation for Yom Teruah being seen as a Rosh HaShanah (new year), I found many references to pagan and Babylonian backgrounds; have we maybe turned Yom Teruah into a day it is not, or does the Tanach provides us proof it is a Rosh HaShanah and should be celebrated is the way we do nowadays?