Your question is a valid one and the missing piece of information that both answers your question and justifies the study of physics itself is a reductionist postulate to the effect that valid explanations of the most basic and most decomposed parts and behaviors of a system can be built into an explanation for all the system's behaviors and emergent phenomena.
Let's see what that means with the practical example comprising:
- On the one hand, quantum electrodynamics, which is what physicists think of as a theory of everything as far as the electromagnetic interaction is concerned;
- On the other hand, the patently true observation that a gecko can effortlessly walk upside down from a perfectly smooth glass ceiling, bearing its whole weight with whatever interaction it uses to stick its feet to surface. Indeed, almost any kind of surface, no matter how smooth, presents no problem for the gecko. The gecko can switch this reliable interaction on and off at will to lift his or her feet or arch the forward half of its body away from the surface to snatch and gobble up a passing flying insect, all the while its hinder half is anchored soundly to the surface by its hinder feet. Almost certainly there are no secretions of any kind of "glue" involved.
We postulate that what we are seeing in the case of the gecko is an quantum electrodynamic interaction - a van der Waals force - between nanometer scale hairs on the gecko's feet and the anchoring surface. What evidence do we have for this?:
- It seems plausible;
- We have partly replicated the effect in synthetic materials and theories of polarizability of molecules in the presence of their neighbors - a QED effect - seems to be an effective way of developing this technology;
- We have no evidence that there is anything other than an emergent phenomenon from the basic QED interaction involved;
- So we apply Occam's razor - the physicist's pragmatic resource management doctrine that says you don't spend resources chasing down a more complicated explanation unless you really need to.
But actually proving we can get a mathematical description of the gecko foot system beginning with basic QED calculations and building them up into a complete description of this particular emergent phenomenon: that is another matter altogether. Actually applying the theory of QED to a description of the interaction of tens of molecules already poses a mathematical problem that is intractable as yet either to our theorists or computing resources.
So, even though we can't as yet give a full QED description of the gecko's feet, I don't think that there would be many physicists around who would seriously think that this would not be something that could in principle be done. And the same goes for many nano- and micro-scale phenomena which are too complex for our basic theories but too small for simple continuum mechanical descriptions to emerge. Even if humans won't have the computing resources to fully describe the gecko's feet from QED for the next hundred years, we still believe that it can in principle be done.
Likewise for a TOE and consciousness. One can get to a stage where one believes that one has a description of the basic interactions and behaviours of the World which everything else - all behaviors including consiousness - emerges from and could be described in terms of - in principle - even though one cannot handle the complexity a TOE description of the emergent behavior.
Compare your question to the highly analogous Church-Turing thesis of the field of computability and foundational mathematics. This is a postulate or hypothesis or dogma made that, through the abstraction of the Turing machine, we understand the foundation for everything that can possibly be computed in principle by conscious humans, even though we cannot at this time know what every future human may be able to reason.