All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If the family of this young man is actually able to kill him if he embraces Islam and he has no choice except to hide his faith in Islam, then, in this case, he may hide declaring his acceptance of Islam till there is no longer a state of compulsion.
As soon as this state of compulsion ends, he has to announce his religion publicly. In this period (in the state of compulsion), he is considered Muslim without committing a sin if his heart is satisfied with Islam. Allah Says (what means):
• {Whoever disbelieves in Allah after his belief... except for one who is forced [to renounce his religion] while his heart is secure in faith.} [Quran 16: 106]
• {Indeed, those whom the angels take [in death] while wronging themselves - [the angels] will say, "In what [condition] were you?" They will say, "We were oppressed in the land..."} [Quran 4: 97]
• {Except for the oppressed among men, women and children who cannot devise a plan nor are they directed to a way -} [Quran 4: 98]
A compelled person is not but a weak who can not avoid fulfilling the will of others.
However, this young man is not permitted to delay his acceptance of Islam even for a moment whether he is compelled or not.
But he is permitted only to hide his declaration of Islam till this period of actual compulsion ends.
Allah knows best.