Dies Natalis Solis Invicti was being celebrated as early as the 2nd and 3rd centuries in Rome. Mithras, whom the Catholic Church imported its version of Jesus from via Paul of Tarsus, shared this celebration with Solis, which would place the celebrations roots easily within the 2nd century.

Keep in mind that the Roman advanced the calendar a day to make Dies Solis (Sun's Day) the first day of the week instead of Dies Saturni (Saturn's Day).

This is not a theory. It's history.