Q: How can we be sure that Brahman is transcendent of the level of appearance? How can we rule out the possibility that it is imperceptible due to the limitations of our mind? Could Brahman be similar to that of a higher dimensional being that is non accessible to human minds, but able to be perceived on higher levels of reality? And wouldn’t this then invalidate claims of it being infinite and eternal, given that these are constructs built on the idea that Brahman is non-phenomenal?
Also, how can we make the connection between ishvara (creator), and sakshi (awareful witness)? Are they both referring to the same being? I am confused.
Your first question suggests a fundamental misunderstanding. Advaita (by the very word) states that reality is non-dual. So ‘appearance’ is just that. The world and every (apparent) thing in it is mithyA, which means that it is only name and form of Brahman (which is ‘defined’ as infinite-existence-consciousness). The separation into a ‘transcendent’ reality and an empirical appearance is for the convenience of being able to talk about it. There is ONLY Brahman, so it is meaningless to speak of being able to ‘perceive’ it. There are no ‘higher dimensions’ or ‘higher levels of reality’ There is only ‘reality’, which is Brahman. Time and space are empirical ‘aspects’ of Brahman.
The truth of all of this is not something that is ‘provable’ in a scientific sense. It is ‘realized’ after hearing all of the related material and clearing doubts about it.
Ishvara is the name given to that principle that ‘maintains’ the empirical appearance and manages the cause-effect nature of action (karma). It is also mithyA. Witness (sAkShin) is quite a difficult subject. I have just written nearly 5000 words to explain it in the first volume of my book on ‘Confusions in Advaita’. It is easiest to think of it as that ‘aspect’ which is who you really are. Your first awareness after waking from deep sleep, if you like, is as the witness. It is ‘beyond’ the mind but needs a mind in order to be aware of something else. (Hence the witness is present during deep sleep but not aware of anything since the mind is not active.) You could say that ‘you’ are ‘Ishvara’ but it is better to say that both of these are empirical aspects and are both really Brahman.
As you can see, it is all quite tricky to talk about. Understandable once you realize that you cannot really talk about it at all!