There’s no evidence to prove that Jesus Christ was born on the 25th of December. The early church, in the bible did not celebrate Christmas and nothing of such was ever recorded until around 440 AD that the Christmas was celebrated. The date was not picked as a result of any evidence.
The pagan holiday, Saturnalia, inherited by the Romans pagans from an earlier Babylonian priesthood was used as a celebration of the god of the Sun.
The Christians (the Church) in Rome choose the date of the pagan celebration to interest the pagans into Christianity because the pagans were already used to celebrate on this date.