Those of us of the Christian faith believe that the first Christmas happened the way the Bible says it did. But does the historical record confirm this? Well, aside from the supernatural aspects which are a matter of faith, in general and by loyalty unto death, yes.
It is a matter of Roman historical record that Jesus Christ lived and was crucified. Documents under the Emperor Claudius confirm it, as do other contemporary sources. Was Jesus the only prophet of his day? Was he the only one claiming to be the messiah? No and no.
But there was something special about this simple carpenter from Nazareth. As opposed to other prophets and men of faith who had a following, Jesus Christ was not trying to leverage his following into an earthly kingdom. Nor was he interested in riches. And, as a very special standout, he was not crazy as a Judean bedbug. All of that from contemporary sources.
The Roman and Jewish records say nothing about his birth, his youth, and very little about his ministry. We can surmise his message was a threat to the political power of the local authorities, but actually not to the Romans. His condemnation by the Romans and crucifixion by them was, or so they thought, more to do with keeping the peace than anything else. For the Romans were, as long as you rendered unto Caesar proper taxes and facetiously official obeisance, a liberal empire and left sleeping dogs alone if they could.
But perhaps the most eloquent testimony, to reference C.S. Lewis, of the life and work of Jesus Christ is the manner of death of his disciples. Many went to gruesome deaths, including those who knew him, rather than recant their faith. If it was a con or a scam or merely a well meaning universal philosophy, the kind of men capable of that would not have sacrificed their lives for it. That they did is also historical fact.
So, can we verify the details of his birth and much of his life through specific historical detail? That is a problematic endeavor. But do billions worship him as the son of the living God? Yes. Do we know that such a man was born and brought hope and love to the world? Yes. And for many, if not most, that hope and love is the essence of this season and of Christmas Day.