It is natural to suppose that these fundamental entities are in some sense necessary. I don't mean this term to imply that they can be rigorously proven from pure logic (logical/conceptual necessity) or even that we personally can be sure that they exist. What I mean is that they are necessary considered in themselves, that (regardless of what we think or know) if we could only understand the fundamental nature of reality, we would know that they had to exist. They are metaphysically necessary. (This is quite distinct from the sort of conceptual inevitability described in the Chesterton quote previously.)
The way I have stated things, this may seem almost like a tautology, since we have stipulated that these things are the fundamental entities which explain everything else. Given that they are the nature of things, they cannot not exist given the fundamental rules of existence, which is themselves.
Some people, though, would argue for the exact opposite, and say that the fundamental nature of reality, because it cannot be explained in terms of anything else, is just the ultimate inexplicable “brute fact”. They would conceive of it more along the lines of the most wildly contingent thing there is, since it has no particular reason to exist and yet it does. But this way of looking at things doesn't make intuitive sense to me.
If the fundamental nature of existence just happens to exist, with no internal necessity, why should we suppose that it should be at all simple or rational in its effects? If it is completely inexplicable, then there are no constraints. And if it is contingent—meaning something which might either exist or not exist—then it seems strange that there would be no process controlling whether it or something else (or nothing at all) comes into being. If there are brute facts, then the entire world rests on a fluke, and the ultimate nature of reality is completely arbitrary and irrational.
Furthermore, if anything about the concrete physical world occurs necessarily, because it had to be that way (besides mere truths of logic) then a fortiori the fundamental nature of existence must be like that too.
If the fundamental entities are necessary, then it stands to reason that they are also eternal, since something that exists necessarily cannot come into being, or cease to be, or indeed change in any way. They must just exist timelessly. Besides which, if they explain what happens at all moments of time, it doesn't seem plausible that they should only exist for certain moments of time. For similar reasons, one can argue that the fundamental entities can't be limited to just one region of space. Their influence must be present everywhere.
It also seems that the fundamental entities (taken as a whole, if there is more than one of them) must be powerful, insofar as their existence is capable of explaining the existence of all other things.
Power here means causal efficacy (I obviously don't mean force times distance per time in this context!). Earlier I tried to avoid making too many controversial assumptions about causality, but I also argued that the very concept of explanation or “because” involves a certain notion of causality, so if you like you may take the notion of power in this sense. (One needs some concept of causation to say that anything is powerful.)
In fact, the fundamental principle(s), taken together, must be all-powerful, and that in two different senses: (1) all the other powers that may exist in the world are explained by reference to theirs, and (2) nothing outside of themselves can prevent them from doing things, because there IS nothing outside of them; only themselves and things whose natures are, by stipulation, subject to their dominion.
This does not, however, prevent there from being constraints on what these beings can do, based on them having some type of definite nature, which only does certain things. And, since everything that exists obeys the rules of logic, it is clear they cannot do logically absurd things, such as causing themselves to never have existed. So none of those silly logical puzzles about whether an omnipotent being can make stones too heavy to lift are relevant here.
All of the metaphysical reflections above, I would endorse whether or not I believed in God. Nothing I have yet said is designed to discriminate between Naturalism and Supernaturalism.