Only 10 Months at First

The story is, Romulus, the first king of Rome, oversaw an overhaul of the Roman calendar system around 738 BCE. The resulting calendar, whose structure borrowed heavily from the ancient Greek calendar system, had only 10 months, with March (Martius) being the first month of the year. The winter season was not assigned to any month, so the year only lasted 304 days, with 61 days unaccounted for in the winter. The New Year was determined by the coming of Spring (or vernal) equinox, days and nights are approximately twelve hours long (equal), with day length increasing and night length decreasing as the season progresses.
Martius31
Aprilis29
Maius31
Iunius29
Quintilis31
Sextilis29
September29
October31
November29
December29

Republican Calendar Adds January and February

Following another calendar reform, which later Roman writers attributed to Romulus’ successor, Numa Pompilius, the Republican calendar was instituted. To account for the days of winter, two additional months were introduced: Januarius and Februarius.
You can see below the beginning of the months names even state their position.

Sept(7)ember: seventh month

Oct(8)ober: eighth month

Novem(9)ber: ninth month

Decem(10)ber: tenth month

January the 11 month

February the 12th month, the last month of the year that changes from 28 to 29 days trying to make up for the errors in the calendar syncing with the natural time of the Sun.

So then  MARCH 1 should begin the NEW YEAR!!  (Wait! Spring Vernal Equinox is usually later in the month of March?, Maybe we should just throw the calendar away and watch the sky. ) :)

Probably should watch the sky but until then March 1 is still much closer to the true New Year than January 1.

Just rip January and February off the front of your calendar and stick it in the back. Much better.

Also research Ides of March:
It was was notable for the Romans as a deadline for settling debts. In the earliest calendar, the Ides of March would have been the first full moon of the new year. March was also the occasion of the Feast of Anna Perenna, a goddess of the year (Latin annus) whose festival originally concluded the ceremonies of the new year. The day was enthusiastically celebrated among the common people with picnics, drinking, and revelry.