Is it permissible for my young brother to shave his beard so that it becomes bushy and not bad looking when he becomes older, so that he can let it grow?

All perfect praise be to Allaah , the Lord of the worlds. I testify that there is none worthy of worship except Allaah  and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

It is not permissible for a Muslim – whether he is young, middle-aged or old – to shave his beard. It was narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Do unlike the polytheists; trim the moustaches and let the beards grow." [Al-Bukhari, Muslim and others]

A person who reaches the age of puberty has become eligible for religious obligations and he is held accountable like an adult.

Therefore, it is not permissible for your brother to shave his beard under the pretext that he is still young. The reason which you mentioned for shaving the beard is not a Sharee'ah-approved justification. That is because the relevant Sharee'ah texts prove the obligation of letting the beard grow and there is no command to try to make it bushy.

Allaah Knows best.