Short answer: No but also Yes!
The Bible does not teach that Jesus was born on December 25th, but the evidence is clear and strong that the time of His birth was about October 1st. It is generally recognized that Jesus was crucified on Friday, April 3rd, A.D. 33. The fact that His crucifixion occurred at the close of the fourteenth day of the month Nisan, and that this date rarely falls on Friday, but did so in the year A.D. 33 substantiates that date. Even Usher, who adopted B.C. 4 as the date of Jesus' birth, was forced to admit that His crucifixion was A.D. 33.
Our Lord was thirty years of age when He began His ministry, and His ministry was for three and a half years only. This generally conceded fact is proved by Daniel's prophecy (Daniel 9:25-27) concerning Christ's cutting off in the middle of the seventieth week of Israel's favor. The "seventy weeks" (A day for a year–490 days, or 490 years–Ezekiel 4:6) dating from 454 B.C. terminated A.D. 36. In the "midst" of that last week of seven years, the "seventieth week," Christ was "cut off" –crucified–April 3d, A.D. 33. As the Lord Jesus was thirty-three and a half years old when He died, we have only to measure back that length of time to the date of His death. The date of His birth would therefore be about Oct. 3rd, B.C. 1.
The early church did not celebrate Jesus’ birth. December 25 became the traditional date of Christmas when it replaced the heathen cerebration of the birth of the Egyptian sun god, Mithra. According to the Julian calendar, the winter solstice fell on December 25. In Egypt, people would rejoice that from that point on the hours of sunlight per day would increase. December 25th., the holiday of the Nativity of the Sun, celebrated this solar event.
Historically, Christians were also happy to note the longer periods of daylight, even though they did not worship Mithra. Since celebrating the winter solstice was a very popular holiday, the “Christian” church chose to replace the Mithra nativity with the nativity of Jesus.
Let us remember: Jesus did not tell his disciples to celebrate his birth. Therefore, it is not important when we choose to remember this wonderful event. Because love and appreciation for our Savior abound in people’s hearts on December 25th, we may join in their attitude of glad remembrance. And the habit of giving gifts to one another seems especially appropriate. God is the giver of every good and perfect gift. Certainly, amongst all His gifts, the one of greatest important to us is the gift of His Son to be our Redeemer.