The time of Jesus birth was at the Fall Feast of Tabernacles. ( He tabernacles with us, God with us, His name Emanuel, God with us) Not The Jewish new year. He was born in a booth that was commanded from God that the Jews do during the feast of booths. The table inside the booth that they put the holy bread on is called a manger. (Jesus, bread of life placed on a table, manger) Just wanted you to know so we can more accurately celebrate our Wonderful Lord!
You say this like you know it’s the truth, when in fact there is no consensus among believers as to which Fall Feast it is. I can present a case for a Rosh Hashanna birth that’s every bit as convincing as your case for Tabernacles. That’s why I said it’s the most likely date without insisting on it. I think the most important thing is that the two major opinions on His birth are within 2 weeks of each other in the early fall.