Luke 2: (KJV)
7 “And she brought forth her firstborn son, and wrapped him in swaddling clothes, and laid him in a manger; because there was no room for them in the inn.”
Compare to Matthew 1: (KJV)
24 “Then Joseph being raised from sleep did as the angel of the Lord had bidden him, and took unto him his wife:” 25 And knew her not till she had brought forth her firstborn son: and he called his name JESUS.”
KJV has translated the “took unto him his wife” literally from the Greek even though the context probably means “took home his wife” as some versions translate.
Even without the “home” translation the implication in “Matthew” is that Jesus was born at home.
“Luke” reports that Jesus was born in a manger.