Rot. Swaddling a child (binding them in strips of cloth, which was thought to help the bones grow strong and straight) was VERY commonly practiced, among very much alive infants, at least up until the 1500s in Europe.
It was emphatically NOT reserved only for burials - tell me, what parent in their right mind would be so unspeakably ghoulish as to wrap a living, healthy baby in burial clothes? It would be like these days putting a wee babe in a coffin-shaped cradle!
As for it being a ‘sign’ - you really think there were any other newborns in stables in Bethlehem at the same time? Of course not, it just wasn’t that big a place. The being in a stable was more than enough.
Same goes for the Magi’s gift of myrrh - people say ‘it prefigured Jesus’ death, since it was used for burials’. No, it WAS used for that, but was used for a heck of a lot of other things besides. If you read Proverbs 7:17, for example, you’ll see a harlot speaking of having scented her bedlinen with myrrh among other things. So it was a valuable gift, but not exclusively associated with burial.