Is there any evidence for this?
We can probably date 25 Dec as Christmas back to the 3rd C, but AFAIK no evidence of celebrations this early. Even the dating requires a degree of inference from sources rather than being directly stated.
I compiled some of the more recent scholarship on the issue in this thread:
Christmas 25 Dec: Scholarly views
Always interested in additional sources though.
It's getting harder and harder to find the websites that document that there were in the third century competing dates for the Feast of the Nativity, and that December 25 was one of these dates, meaning that it was celebrated on that date by some of the churches but not all. Increasingly, websites are focusing in more on the fact that it was in the fourth century that the church in the west decided as a whole to celebrate it on December 25, so that everyone would be on the same page. An early second century date would of course put a December 25 Christmas decades before the formation of the holiday of Sol Invictus. Here's what I've been able to find for you.
It was Hippolytus of Rome (170-235 CE) that spoke of Christmas being on December 25. "Hippolytus, a younger contemporary of Clement, does state that the Nativity had occurred on December 25 (
Commentary on Daniel, IV.23.3). And, although the statement may be a later interpolation, he reiterated several decades later (in AD 235) that Jesus was born nine months after the anniversary of the creation of the world, which Hippolytus believed to have been on March 25 (
Chronicon, 686ff). The Nativity thus would be on December 25."
Sol Invictus and Christmas
Here is another good reference: "Third century theologians reckoned that the world was created on the spring equinox, and four days later, on March 25th, light was created. Because Jesus coming signaled a new beginning, or new creation, it made sense to assume that Jesus conception would have also been on March 25th. This would place the birth date of Jesus nine months later, in December."
Is December 25 the Actual Birth date of Jesus? - Jerry Robinson Ministries
Here is another one. "But the December 25th date could have come from Roman Catholic historian, Sextus Julius Africanus. In AD 221, he dated Jesus’s conception to March 25—nine months before December 25."
Is December 25 the Actual Birth date of Jesus? - Jerry Robinson Ministries
"Was there any theological reasons for choosing December 25th as the birth date of Jesus? Third century theologians reckoned that the world was created on the spring equinox, and four days later, on March 25th, light was created. Because Jesus coming signaled a new beginning, or new creation, it made sense to assume that Jesus conception would have also been on March 25th. This would place the birth date of Jesus nine months later, in December."
Is December 25 the Actual Birth date of Jesus? - Jerry Robinson Ministries
Crosswalk sums up the development of Christmas as follows: "It was not until the third century that various pockets of Christians began to show interest in the date of Christ’s birth, and it would take another century for the Church to begin celebrating it with some uniformity." The "pockets" refer to the variety of dates used in the third century, December 25 among them. "Uniformity" refers to what I was saying about the western church settling on Dec 25 for all the churches.
Was Jesus Really Born on December 25th?
This website has a section on the second century, and says, "Interestingly, the Church later recognized March 25th [ALSO used by the chruch at that time as 1. they day for the creation of the world and 2. the day of Jesus resurrected -- Easter] as the Annunciation (the date that Gabriel appeared to Mary to announce the birth of Christ and also believed to be the moment of conception (notice the pro-life implications) and December 25th as the birthday of Christ." It also says, "Most Christians assume that the Annunciation was determined by taking the date of Christmas and counting back nine months. On the contrary, it was probably the reverse." IOW, the feast day that honored the conception of Jesus came first, followed by establishing December 25 as the feast day of the Nativity as being nine months later -- the time of a pregnancy.
I'm sure if I spent a couple of hours perusing the internet, I could find more, and better, sites to document this. It's not worth that sort of effort to me. I hope this will be good enough.