Why "later"? Paul wrote to Timothy:
NKJV
1Ti 1:15 This is a faithful saying and worthy of all acceptance, that
Christ Jesus came into the world to save sinners, of whom I am chief.
He didn't write, "Jesus came into the world to save sinners, and later was called Christ/Messiah."
Matthew writes of His birth as "the birth of Jesus Christ":
Mat 1:18 Now the birth of Jesus Christ was as follows: After His mother Mary was betrothed to Joseph, before they came together, she was found with child of the Holy Spirit.
Luke also, in recording the words of the angel to the shepherds, wrote:
Luk 2:11 For there is born to you this day in the city of David a Savior, who is Christ the Lord.
Nothing there about being called the Christ, the Messiah, later.