What is the earliest reference to Christmas’s being celebrated on December 25?

In the middle of the second century, Christians in Antioch were already celebrating Christ’s birth on that day.

The day was not officially recognized by the Church as the date of Christ’s birth until A.D. 350.

Why December 25?

The day was formerly celebrated by worshippers of the god Mithra as the Dies Invicti Solis, or “Day of the Invincible Sun.”

It seemed natural to Christians to replace Mithra with Christ, called in the Bible the Sun of Righteousness.