Making one's excuse accepted by Allah

wa alaykumassalaam

Check with the local masjid prayer timing. Even if you can not go there for any reason, you can still follow their prayer timing.

You can pray salah Fajr as long as it is still Fajr. So let's say Fajr starts at 3:03 AM and sunrise at 5:30 AM, you can pray salah Fajr at 5 AM and it will still be valid.


If you wake up to offer salah but too sleepy :

Aishah narrated that :
Allah's Messenger said: "When one of you is sleepy and he is performing Salat, then let him lie down until the sleep is gone from him. For when one of you performs Salat while he is sleepy, perhaps he wants to seek forgiveness but he curses himself." (Jami'at-Tirmidhi)


Guard your salah, it's the first thing you will be held accountable for on Judgement Day with Allah :

On the authority of Abu Hurayrah (may Allah be pleased with him) from the Prophet (ﷺ), who said:
Allah (mighty and sublime be He) says: The first of his actions for which a servant of Allah will be held accountable on the Day of Resurrection will be his prayers. If they are in order, then he will have prospered and succeeded: and if they are wanting, then he will have failed and lost. If there is something defective in his obligatory prayers, the Lord (glorified and exalted be He) will say: See if My servant has any supererogatory prayers with which may be completed that which was defective in his obligatory prayers. Then the rest of his actions will be judged in like fashion. It was related by at-Tirmidhi (also by Abu Dawud, an-Nasa'i, Ibn Majah and Ahmad).