December 25 is the traditional anniversary of the birth of Christ, but most scholars are unsure about the true date for Christ’s birth.
For the first few centuries of Christianity, Christmas was not celebrated and lacked a specific date. After all, the Bible does not give a specific birth date for Jesus.
What is probably the first mention of Jesus’ birth on December 25 dates back to the 3rd century, when Hippolytus of Rome wrote, “The first advent of our Lord in the flesh, when he was born in Bethlehem, was December 25th, Wednesday” (Commentary on Daniel, tr. by Schmidt, T. C., 2010, Book 4, 23.3). The earliest mention of some sort of observance on that date is in the Philoclian Calendar, representing Roman practice, of the year 336. 
According to History.com, Dec. 25 was likely chosen by church officials as a way to help evangelize pagans who celebrated different observances on that date.
“When church officials settled on December 25 at the end of the third century, they likely wanted the date to coincide with existing pagan festivals honoring Saturn (the Roman god of agriculture) and Mithra (the Persian god of light),” noted History.
“That way, it became easier to convince Rome’s pagan subjects to accept Christianity as the empire’s official religion.” 
The church leaders in Rome decided to celebrate Christ’s birth during the winter solstice in an attempt to Christianize these popular pagan celebrations. For the most part their efforts failed to make the people conform, and the heathen festivities continued. Today we find ourselves left with a bizarre marriage of pagan and Christian elements that characterizes our modern celebration of Christmas.
Regardless of the pagan background of so many December traditions, and whether or not Jesus was born on December 25th, our goal is still to turn the eyes of all men upon the true Creator and Christ of Christmas. The light of the world has come. And the Christmas season and celebration presents the church with a wonderful opportunity to preach the good news–that men can be made righteous and have peace with God through faith in His Son, Jesus Christ.
Source: 1. https://www.christianpost.com/news/7-interesting-facts-about-christmas.html?page=22. https://www.gotquestions.org/December-25.html3. https://www.gty.org/library/questions/QA68/why-do-we-celebrate-christmas-on-december-25