I'm going to suggest that reconstructing the authentic scene of the birth can come from noting the curious fact that the manger is mentioned three times in the account of Jesus' birth. For all the charm of the traditional Creche, the actual biblical text supports a different scene, one in which "The Manger" is the key to the story.
The Birth of Jesus - Manger #1
The Gospel of Luke tells us that Mary and Joseph arrived in Bethlehem to be enrolled in a census:
"While they were there, the time came for her to give birth. And she gave birth to her firstborn son. She wrapped him in swaddling clothes and laid him in a manger (ἐν φάτνῃ; en phatne), because there was no room for them in the inn." (Luke 2:6-7)
The Greek word rendered "manger" is φάτνῃ (phatne). The word could denote the feeding trough itself or the stable where an animal would be housed for eating and sleeping.
Manuscripts of the Greek New Testament, which were copied by hand for hundreds of years before the invention of the printing press, contain thousands of minor (and also some major) variations. One interesting variation is that some manuscripts, indeed the very one considered the authoritative text of the Greek Orthodox Church, don't say that Mary laid him in a manger, but rather that she laid him in the manger (ἐν τῇ φάτνῃ; en te phatne).
The account in Luke continues with the appearance of the Angels to the Shepherds. We might have thought that the reference to Jesus being in a/the manger was extraneous. But the Angels seem to think it is the primary information the Shepherds need to find the new-born Messiah:
"You will find an infant wrapped in swaddling clothes and lying in a manger." (Luke 2:12)
Again, some ancient manuscripts have "the manger" (ἐν τῇ φάτνῃ; en te phatne) here as well.
How Did the Shepherds Know Where to Find Jesus?
If you Google on the question of "How did the Shepherds find Jesus?" you may find the claim that the shepherds must have known of a passage in Micah 4:8, which led them to a specific tower near Bethlehem. This is a contrived and unconvincing solution to the problem. I suggest the answer is more straightforward. The shepherds knew where to find Jesus because the Angels told them exactly where to go.
The shepherds hastened to Bethlehem and we learn that:
"They found Mary and Joseph, and the infant lying in the manger (ἐν τῇ φάτνῃ; en te phatne)" (Luke 2:16).
It is significant that, in this third instance, all the manuscripts include the Greek definite article τῇ (te) "the" here. It was the manger. The manger is what they knew to go to, in order to find Jesus.
And it becomes conspicuously strange for the manger to be mentioned again for this third time. I conclude that, after Mary gave birth, she laid Jesus, not just in some random feeding trough in some random stable, but apparently instead in something known to the people of this area as "The Manger." And people of this region knew exactly where "The Manger" was.
What was "The Manger"?
I suggest, based on early Christian evidence and modern parallels, that "The Manger" was some type of rock formation locals knew was found in a nearby cave. It was likely in the shape of a feeding trough, hence its name.
My great-grandfather Lance Dodge was the man who set the dynamite that blew open the entrance to the Cave of the Mounds, in Blue Mounds, WI. Inside that pristine cave there are natural rock formations that are named from their similarity to other objects.
So, for instance, there is a rock called "The Parrot." Another formation is called "The Lilly Pads." In the Wisconsin Dells, you can see a rock formation known as "The Piano" because of its shape.
The earliest Christian traditions about the location of Jesus' birth state that he was born in a cave. The 2nd Century AD Christian writer Origen tells us that the place was a site for tourism of both Christians and non-Christians:
"There can be seen the cave located in Bethlehem where he was born and the manger where he was wrapped in swaddling-clothes. And this site is talked about with great interest in all the surrounding countries. Even among the enemies of our faith it is being said that in this cave Jesus was born, the one who is worshiped and revered by the Christians." (Against Celsus 1.51)
Origen is a particularly important witness to the fact that, not only was the cave still something to see and visit, but also the manger was still there. He makes no mention of this cave ever having been a stable. His testimony suggests that the manger is indeed some geological feature within the cave that would have been preserved for over a hundred years after the birth of Jesus.
The Emperor Constantine had a Church constructed over the site of this cave. Today there is a Silver Star marking the traditional site of the birth of Christ. Knowledge that a geological feature in the shape of a feeding trough had once been the cradle in which Mary placed the baby Jesus would have long since vanished when workers cleared the area for the construction of a pilgrimage site.
Even so, I believe the evidence I have described here presents a compelling new way to interpret the Nativity Story.