Matt dreams of the Garibaldi

If your Bible is infallible, can you explain why in the New Testament in Matthew, while describing the Jesus birth story the author managed to get something so simple as the reign of King Herod and the Roman Census so badly wrong. You see Herod died in 4BCE and the Romans held the first Census in 6CE. Now that's a 10 year gap. Then not only did they get that part wrong but they entirely fabricate the Massacre of the Innocents story. Then In the Old Testament the Exodus story, more fabrication. At the time of its occurrence there were 3 great empires in the region. The Egyptian, the Hittite and the Babylonian. And not one of them recorded the mass movement of an estimated 2.5 Million people, nor is there any any physical evidence of such a movement ever been found. And then we have Moses himself, who supposedly went up a mountain (that nobody today can find) spent a month up the mountain by himself (not eating or drinking), who was spoken to by a burning bush, and with no tools (a hammer and chisel), carved the commandments (given to him by the burning bush), into stone slabs and then carried them down the mountain.