…”Not only this, the prophets of God are also blessed with the light of innate guidance – the light which every person has been blessed with – in its most ultimate form. They always keep its flame fully alight and shield it from the storms that arise within man’s inner-self. Thus before they are blessed with divine revelation from God, their heart and mind are very pure and the truth is already evident to them to a great extent. The Quran calls this state of their inner enlightenment as بَيِّنَةٌ (bayyinah). It is evident from various incidents from the lives of the prophets that they present divine revelation as an evidence for this inner enlightenment and the vision they possess“…

See this for details:

Discussion 16080

Allah’s ilm which is absolute, perfect and exists beyond the realm of time and space. In this very Allah’s ilm, beginning of life on earth, its end, the prophethood of prophets, Jannah and hell are not bound by limitations of past, present and future. Therefore, the prophethoods starting from Adam (AS) to Muhammad (SWS) were all existent in Allah’s ilm even before the birth of these prophets, just like His ilm occupies our start and our end. But to reach this end, a person has to use his freewill for his own itmam-e-hujjat for the day of judgement and his guidance and misguidance depends on the same law, same is the case with Prophets.

It is not that after speaking as an infant, Jesus (as) continued to talk regularly. To some extent, you can understand this with reference to Ehd-e-alast, where the memory of that event was erased. Jesus (AS) grew up normally and reached to a point where He was given proper prophethood with the objective of completing final itmam-e-hujjah on Bani-Israel.

Speaking of Prophet Esa (AS) in his infancy was a miracle which served two purposes (all miracle have a purpose considering the effectiveness of the holistic scheme of God in the given circumstances):

i) It saved Maryam (AS) from accusation of adultery.

ii) It served as a message to Bani-Israel (as can be seen in Bible as well [1]) because it was going to be final Adalat for Bani-Israel and they were to face eternal punishment for their transgressions and that is the reason Jesus (AS) has been called a sign of Qiyamah.

If I were to sum it up:

– Jesus (AS) just like every other Prophet was prophet in God’s Knowledge, therefore, speaking at infancy doesn’t mean that his prophethood was given to him at the moment when he was born.

– Just because He spoke in infancy based on Allah’s izn and ilm, doesn’t mean he didn’t have to grow up like other prophets who valued that innate guidance and reached apex of piety through the same law of guidance and error.

– Speaking of Jesus (AS) was a miracle that served two major purposes and it was not meant to give him effective nabuwat at that time.

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[1] Matthew and to some extent Luke say that news of Jesus’s (sws) birth spread in somewhat these words “King of the Jews has been born; a promised Messiah who will restore the kingdom of Israel“. Such news disturbed King Herod, who was the Roman ruler at that time; so he ordered all boys of two or below the age of two to be killed. According to Matthew, King Herod found out about Jesus by one magi who studied stars and had come from the east to see the newborn Messiah. They first asked about him at Herod’s court in Jerusalem and then they followed the light of a star to Bethlehem. The star went ahead of the magi and “stopped over the place where the child was”: (seems to be pure romantic literature, as one critic puts it, as no scientific contortions will deal with the behavior of this star except if one is willing to believe in retrograde planetary motion). There they found Jesus and gave him gifts of gold.

The Quran says that after his birth Mary (sws) carried Jesus (sws) in her arms, and returned back to her own people. According to Quran:

They said: O Mary! Indeed you have brought a thing that is mighty unheard of. O sister of Aaron, Your father was not a man who used to commit adultery nor your mother was an unchaste woman. Then she pointed to him. They said how could we talk to one who is child in cradle. He (Jesus) said: Verily I am a slave of Allah, He has given me the scriptures and made me a prophet. And He made me blessed where so ever I be, and has enjoined on me prayer, and charity as long as I live. (19:27-31)

It was probably this miracle, Jesus (sws), speaking in the cradle, which spread as the news that a “Saviour” of Israel has been born. This could have urged Herod to search for the baby and that ultimately led to flight of Mary (sws) with Jesus (sws) to Nazareth.