I though that I commented on this, but now I don't see it. Anyways, it is not healthy to wake up that early, you need at least 7,5 hours of sleep.
It is possible to vibrate mantras in your head, or very silently, or filter outside noises out(you need a lot of practice for that), or meditate outside, or something.
Maybe tell your parents you want to do yoga? You don't need to tell anything else, yoga is pretty common nowadays.