According to this from Wiki, it was just a little ealier - but not much.
The earliest reference to the celebration of the nativity on December 25 is found in the Chronography of 354, an illuminated manuscript compiled in Rome.
remember Christianity was suppressed for centuries; where it was celebrated, people would have been wise not to talk about it. Given the randomness of surviving records on most topics from those days, absence of evidence isn't evidence of absence.
"the 6th century monk Dionysius Exiguus created the B.C./A.D. system of dating based on the birthdate of Christ. His calculations were not very good. Dionysius had Christ born on December 25, 1 B.C"