Can a Male who is not grown up yet be an Imam? What is the proof from the Qur'an and Sunnah? If this boy is better than the other prayers in reading Qur'an can he be an Imam?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

The imamate (leading a prayer) of a discerning boy is acceptable according to al-Shafi'e, but disliked in Malik 's opinion. According to the well-known opinions of Abu Hanifa and Ahmad , the imamate of a discerning boy is acceptable only in optional prayers.
As for scholars who permit this action, their proof is: the Hadith of Amr Ibn Salamah (Radiya Allahu Anhu) that relates the imamate of Amr of his tribe while he was six or seven years old as recorded in Sahih al-Bukhari.
It is not acceptable to object to the above opinion with narration of Abdul Razzak from Ibn Abbas : "A boy should not lead a prayer unless he becomes pubescent" , since Ibn Hajar considers this Hadith with weak chain of narrators.
Then, according to those who legalize the imamate of the boy, he should be the most versed in the Qur'an for the Prophetic Hadith: "Let the one who is most versed in the Qur'an lead people in prayer" . [Reported by Imam Muslim and Ashaab al-Sunan].
Abu Hanifa and Ahmad believe that it is possible that 'Amr was leading his people in optional prayers since he was not required to perform the obligatory prayer, nor does a congregational prayer become valid by his presence. But, the same Hadith disproves this opinion since the Prophet (Sallallahu Alaihi wa Sallam) said: "When a time of prayer has begun, one of you should make Azan, and then, the one who is most versed in the Qur'an should lead you" .
The narrator 'Amr said: 'My tribe found no person more versed in the Qur'an, so they asked me to lead them in prayer' .
As a result, there is no doubt that the imamate of the boy is permissible in obligatory and optional prayers. This is because of the Prophet's (Sallallahu Alaihi wa Sallam) expression: "When a time of prayer has begun" that indicates that the obligatory prayers and their like are included in the meaning of this expression. In addition, there is no need to make Azan for optional prayers. Furthermore, since the Prophet (Sallallahu Alaihi wa Sallam) ordered them to pray in a congregation means this prayer is one of the five obligatory prayers.
The Prophet (Sallallahu Alaihi wa Sallam) did not order his companions to perform optional prayers in a congregation. In fact, there is no proof in the saying of: the Prophet (Sallallahu Alaihi wa Sallam) did not know the doings of those who permitted the boys to be Imams. Then, it is completely wrong to think that the companions sanctioned something wrong and the Qur'an was being revealed as recorded in al-Bukhari and Muslim from Jabir : "We were practising coitus interrupts during the age of the Prophet (Sallallahu Alaihi wa Sallam) and the Qur'an was being revealed" .
Allah knows best.