It is an interesting question. Some people who are pursuing the so called "theory of everything" have suggested that it may be unique. That is, it may be that there is only one way that such a theory could be formulated (or one collection of functionally equivalent ways, perhaps) and so there might be a way to derive everything from first principles.
The poetic way this is sometimes expressed is to wonder if God had any choice.
As yet, this has certainly not been demonstrated. Only speculated.
But there is a strong line of thought that a very small collection of observed things should be able to nail down just about everything about such a theory. You start with some such thing as the beginnings of Leibniz's ideas about monads. And you add in some interactions. And it seems that these interactions must have certain kinds of symmetry to look even vaguely like what we see. And having done that we seem to be able to get a large portion of the standard physics model. That is, certain symmetries seem required, and that's a large part of the story.
Notice the "what we see" bit there. So far, we still seem to need to look at things, somehow, a little at least, to get anywhere in physics.