I have a secret for you.
January 1 has NOTHING to do with any modern religion.
It is from Roman times.
Ancient Roman calendar, representing the winter solstice. (Before Gregory, 450 years ago, jan 1 was the winter solstice).
Just like midnight starts the new day for them, so too, the winter solstice, comparable to the yearly midnight, is the when the year starts.
By the way, December 25, or January 6, has nothing to do with any modern religion either, but that us a whole ‘nother story.
It was actually a day of death destruction of jews in ‘honor’ of the god january is named after. See Rabbi L. Keleman’s lecture on TorahAnytime
On the topic of January, the Yerushalmi in AZ, first Mishna, says a possible story about why they named it January.