In Luke 1:41, 44; 2:12, 16, we find that the Greek word translated "babe" is βρέφος (brephos), and in these verses, the meaning is either "an unborn child" (1:41, 44) or "a new born child" (2:12, 16). But in recording Jesus' circumcision when He was just eight days old, which was according to the Law (Lev. 12:3), Luke used the Greek word παιδίον (paidion). He wrote, "And when eight days were accomplished for the circumcising of the Child, His name was called JESUS, which was so named of the Angel before He was conceived in the womb" (Lk. 2:21). Here, the obvious meaning is "a young child," as it is translated seven times in Matthew 2 (8, 9, 11, 13, 14, 20, 21).
Luke still uses the Greek παιδίον (paidion) to describe Jesus as He grew older, but at the age of twelve, he suddenly uses the Greek παῖς (pais), which is translate "servant" more often than it is "child." He wrote, "And when they had performed all things according to the law of the Lord, they returned into Galilee, to their own city Nazareth. And the Child (paidion) grew, and waxed strong in spirit, filled with wisdom: and the grace of God was upon Him. Now His parents went to Jerusalem every year at the feast of the Passover. And when He was twelve years old, they went up to Jerusalem after the custom of the feast. And when they had fulfilled the days, as they returned, the Child (pais) Jesus tarried behind in Jerusalem; and Joseph and His mother knew not of it" (Lk. 2:39-43). Jesus was now a servant within His family (see Gal. 4:1-2).
We know nothing of the life of Jesus between the ages of twelve and "about thirty" when He was baptized by John (I believe He was anointed for ministry) and confirmed by the Father Himself (Lk. 3:21-23). I believe that at the age of thirty, Jesus was, according to the Law, qualified to serve God as is seen in Numbers 4:3, 23. Jesus had "paid His dues." Hebrews 2:17 says:
"Wherefore in all things it behoved Him to be made like unto His brethren,
that He might be a merciful and faithful High Priest in things pertaining to God,
to make reconciliation for the sins of the people."