Maybe there is no fundamental level
TL;DR: People look for a fundamental theory of physics, but does it have to exist?
The holy grail of fundamental physics is to find a single set of constituents and laws that explain all physical phenomena. The implicit assumption here is that it makes sense for such a thing to exist and it is possible for us to find it. Let’s call it into question: is it possible that no such fundamental level exists?
When we write a physical theory, we are creating a mathematical model to describe a set of physical objects. The model, so far, has always been limited in the sense that it is valid only within certain boundaries. Classical mechanics is what we use to design bridges, airplanes, radio antennas, and most objects we use in day to day life. We know it is an approximation of reality because if we deal with small objects in very precise settings quantum mechanics is needed; if we deal with objects under large gravitational fields general relativity is needed. We also know that quantum mechanics and general relativity are valid within certain boundaries, because the regimes in which they work seem to be incompatible with each other.
A fundamental theory, then, would be a model of reality that would work in ALL circumstances. While all other models are approximations of reality in certain conditions, a fundamental theory is never an approximation: it is the real thing. This is not a difference in quantity, like the transition from classical to quantum, or from classical to relativity. This is a difference in quality, and it is why I think some scrutiny is warranted before accepting that this is even possible. Even more so in light of the following.
Both mathematics and computer science bumped into fundamental limitations. For the first, any formal system will contain sentences that cannot be proven either true or false. For the second, no algorithm exists that can tell us whether other programs terminate or not. These limitations are ultimately caused by the fact that we can only write programs and proofs with finitely many symbols. Can we imagine some sort of limitation along the same lines?
If we look at established modern theories and proposals for newer ones, they are intrinsically more complicated than the older ones. The mathematical structures are more complicated (e.g. Hilbert spaces, pseudo-Riemannian geometry, … ) and span more variables (e.g. field theories, increasing number of dimensions, … ). We can imagine, then, that a more complicated model can give us a better description. But we can also imagine that any model written with finitely many symbols cannot capture the entire complexity of the universe. There is no reason that the rules of nature allow a description that fit in finitely many symbols. We can also imagine that the number of symbols needed to write the model increases exponentially with the precision of the model.
We could go over other more tangible reasons as to why a single fundamental theory may not be possible, but the goal is not to discourage those efforts. The goal is to encourage critical thinking of implicit assumptions. It is a lot more valuable if you come up with your own reasons as to why such an effort may not pan out.