The history of the Roman calendar is somewhat unclear. The Julian reform is well-attested, as is the immediately pre-Julian calendar. This latter calendar is 12 months starting with January with day lengths of 29/28/31/29/31/29/31/29/29/31/29/29, plus an occasional intercalary month of 27 days whose insertion caused February to shrink to 23 days.
The Romans themselves maintained that before the Republican calendar, the year consisted of 10 months of alternating 30/31 days, with the winter months (of what would be January and February) consisting of a vague collection of days omitting a fixed month. But this explanation is dated essentially to people writing "what we used a millennium ago," and there's no attestation of this calendar much closer to its usage period.
In any case, it's definitive that the year used to start in March. When and why it transitioned to January is unclear. For what it's worth, even after most of Western Europe transitioned to using a Julian calendar, the starting date was quite inconsistent until very late. (England only switched in the 18th century, at the same time it adopted Gregorian calendar).