How does the angel proves that Jesus was the messiah at his birth in Bethlehem?

Simply by his proclamation from our Father in heaven, written for us in Luke 2, which said -10. And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, which shall be to all people.

11. For unto you is born this day in the city of David a Saviour, which is Christ the Lord.

12. And this [shall be] a sign unto you; Ye shall find the babe wrapped in

swaddling clothes, lying in a manger.