The first evidence of the observance of a "Mass of Christ" was in Rome, 336 A.D. and earlier Christians do not appear to have given any credence to the commemoration of the nativity.
Origen of Alexandria in fact strongly opposed the celebration pointing out that scripture only indicated 2 birthday celebrations....Pharaoh and Herod. In both cases it was an occasion for an execution. Origen came of age in the 3rd century A.D.
The December date for the holiday probably arose from a desire to provide an alternative to Roman "Birthday of the Unconquered Sun" and the Persian birthday of Mithras, both of which were celebrated around the winter solstice.