Matthew includes stories about Jesus that heavily borrows from the story of Moses, a folklore character of Judaism, that within the book of Exodus borrows from Mesopotamian hero mythology motifs such as being born into poverty, escaping infanticide, running off to the protection of Egypt, preaching law from a mountainside, etc. These details likely never historically happened to any leader of any Hebrew exodus from Egypt, but they are ancient Eastern ways of saying: "This is a deliverer." Matthew adapts these earmarks into his narrative for what appears to be a Jewish audience, marking much of his infancy narrative as mythology.
Luke's infancy narrative is also mythology. It literally changes the language from the Koine Greek of the 1st century to the Greek of the Septuagint after its introduction to Theophilus in chapter 1 through the ending of chapter 2. It includes visits from the angel Gabriel, who is featured the most in Greek Jewish texts like the expanded Book of Daniel and especially the Book of Enoch. And in the infancy narrative of Luke, the characters break out in song as if they were in a musical, something we don't see in the other gospels. This is also a clue that the author is not being literal nor even cares to be taken that way.
In Matthew chapter 21, the author has Jesus ask his disciples to get a donkey and a colt for him to fulfill the prophet's words for his ride into Jerusalem. This is obviously a mistake that the other writers do not make (see for instance Mk 11:2) and evidence that the author of Matthew was neither an eyewitness nor even Jewish. This is a poor reading of Zechariah 9:9 where the "savior" rides on "a colt, and the foal of a donkey." The "colt" and "donkey" are the same thing in this verse, written just as a poem. But "Matthew" misunderstands. Obviously, the "triumphant ride" into Jerusalem of Matthew is thus a fabrication--at least the one in Matthew. Whether the rabbi Jesus of Nazareth did it at all or did it in a way the gospel writers wanted the Christians to believe all depends.
And that is the point. The gospels are meant to be "believed."