Assalamou alaikum
I do wudu for years in a certain manner. It is as follows: I get up from sleep at night then I turn on the tap and I immediately start with washing my face (then mouth,nose etc). Because I always have read that starting with washing hands is not obligatory (even after sleep at night) in order for wudu to be valid.
But the hadith Whoever gets up after sleeping, let him not put his hand in the water container until he washes them thrice, for he does not know where his hands rested at night.” [Al-Bukhari and Muslim] confused me. Is my manner of wudu which I described above a valid wudu? I know this is not sunnah wudu but is this at least valid? I already have read Fatwa No: 366532 and No: 36103 but they do not answer my question. Please advise me Jazak Allah

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.

Your ablution, performed the way you mentioned, is valid and your prayer is correct. As for the command of washing hands upon waking up from night's sleep, the view of the majority of the scholars is that this is only recommended and not obligation. However, in the future, you should be keen to wash your hands upon waking up, because there are some scholars who consider this to be obligatory.

Allah knows best.