There’s a huge chunk of the universe that is currently not accessible via experiments.
Even when we discover more sophisticated methods, there might be other parts of the universe that are inaccessible to possible research projects carried out by entities, such as humans, within the universe. Knowing anything about the universe requires changing the universe, even if in very slight degrees. Running an experiment means interfering with the target system that I’m investigating because we are in the universe.
Similar things apply to the human mind. Take the overall mental state that I’m currently in. I feel a certain way, I have certain thoughts, I’m trying to answer certain questions, I’m looking at my mental history, and I’m weighing reasons that speak in favor of what I believe (as well as against it) so that I can get a reasonable point of view on my own point of view. As I do this, I change my overall mental state by virtue of thinking about it. This is what is called the paradox of self-consciousness. If I’m conscious of consciousness, if I’m consciously thinking about thinking, I change the state that I’m targeting because my overall mental state is now different. I might use yet another third-order state in order to think about me thinking about thinking, but this makes things more complicated and does not help me to get outside the skin of my thought, as it were.