Certain interpretation of Gödel's incompleteness theorems states that not all truths associated with particular systems can be seen from within the system (this is basically a consequence of liars paradox). Does this suggest that there must always be something more than simply the system itself? Maybe not, it may simply be that not all truths can be known even if they're there. However, if it had to be the case, then perhaps it would be necessary that there will always be more complexity "somewhere out there". Then maybe we could claim that it is necessary that the cosmos (all of existence) is necessarily infinitely complex. Perhaps knowing that the cosmos is infinitely complex, is one of those things that cannot be known. Never the less, if that were the case, it could solve a lot of foundational problems, because in such a cosmos nothing is fiction. We would expect to find anything somewhere within that set, even something like the birth of our universe and emergence of human consciousness.
"Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."
Compared to the previous, questions asked by your everyday physicist seem almost trivial. We can always build scientific models and fit all available observations from our local neighborhood of the cosmos, the observable universe. Sooner or later that is. These models will explain the universe within reason and give rational and justified expectations of how it likely evolved in the past and how it can be expected to evolve in the future. These models are by definition our best guess and they will to the best of our ability serve the goals we have given them.
There remains, however, one deeply mysterious question. What is the nature of consciousness? Since we are the observer, the one who experiences finite rate for the passage of time among other things (generally speaking physics is tenseless as a consequence of general relativity), it is nontrivial to arrive at an understanding of how human consciousness could come to be. We can imagine a machine that externally speaking reacts to stimuli as we do, but it is less obvious what (if any) separates us from such a machine. If consciousness is nothing more than states of information evolving in time at a finite rate (that can be counted relative to some other states such as global entropy), it still isn't entirely obvious how our experience of the present can exist. Is it somehow complementary to something in the universe like certain aspects of quantum mechanics? Or is that too one of those questions that simply cannot be answered from within?
At least it seems quite likely that simply by constructing certain configuration of matter, the matter will acquire consciousness like we do. This is mind the problem might not be so severe. The question then becomes is there something special about the universe that is related to consciousness in some special way? Like nonlocality of quantum mechanics or perhaps the many worlds interpretation? Suppose there isn't anything particularly special about any of this, then in fact the most important postulate waiting for proof (to the extent anything can be proven) might be that the cosmos is necessarily infinitely complex. Given that, everything more or less follows.
The determinism of many worlds interpretation would be less problematic if there was no consciousness, because then there is nothing special about one path over another. What is, is the whole of multiverse. It's consciousness that experiences only one path and one present that is mysterious, because we would like to understand what determines we experience this path instead of some other. Perhaps one could inject free will and consciousness somewhere in there somehow, or not.