One can find, through the writings of Lucretius, a powerful yet simple Epicurean argument for matter's (factual or metaphysical) necessity. In simplest terms, the argument is that since matter exists, and since nothing can come from nothing (in the sense that everything with an originating or sustaining efficient cause needs an originating or sustaining material cause, respectively), matter is eternal and uncreated. The argument can be strengthened in light of the scientific evidence for the conservation laws, according to which it’s at least physically impossible that matter-energy is created or destroyed. And if there are no supernatural beings that can annihilate matter-energy, the latter is at least de facto indestructible. Therefore, given the uncreated, eternal, and de facto indestructibility of matter-energy, it follows that matter-energy (or if matter-energy isn’t fundamental, whatever matter-energy is ultimately made of) is at least a factually necessary being.[1]
A stronger version of Epicurus' core argument can be developed by adding an appeal to something in the neighborhood of origin essentialism. The basic line of reasoning is that if being uncreated is a property of matter-energy in the actual world, then it is an essential property of matter-energy, in which case matter-energy in the actual world is essentially uncreated.
Yet stronger versions of the argument can go on from what is said above by appealing to a strong version of the principle of sufficient reason to argue that whatever plays the role of being eternal, essentially uncreated, and indestructible does not vary from possible world to possible world. But if not, then matter is a metaphysically necessary being.[2] On any version of the argument, however, we seem to get the conclusion that the universe requires no external sustaining cause, in which case, a fortiori, God is not required to play such a role.
The broadly Epicurean line of reasoning above can be seen as a cosmological argument of sorts, but one that concludes that matter-energy (or its ultimate constituents), and not an immaterial creator, is the uncaused cause of contingent, dependent, concrete reality. Let us therefore call any argument that deploys a material-cause version of the principle ex nihilo nihil fit to infer the factual or metaphysical necessity of matter (or matter's ultimate constituents) an Epicurean cosmological argument.
If successful, Epicurean cosmological arguments can be used to provide evidence in support of atheism over theism. For such arguments provide prima facie evidence that matter-energy (or its ultimate constituents) are factually or metaphysically necessary. But if so, then since it’s constitutive of classical theism that God is the creator of any material universe that happens to exist, then since an essentially uncreated universe exists in the actual world, and since essentially uncreated universes cannot, by definition, be created, it follows that the God of classical theism does not exist. Indeed, if, as many classical theists assert, God exists necessarily if he exists at all, then given that he doesn’t exist in the actual world, God exists in no possible world. In other words, God’s existence is metaphysically impossible.
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[1] Another line of reasoning comes from recent work on existential inertia (cf. Beaudoin, Audi, Oppy, and Schmid)
[2] Some other lines of reasoning: (i) The argument from necessitarianism about the laws of nature: Our specific laws of nature are essential to the universe (cf. Swoyer, Shoemaker, Bird et al.), including the conservation of matter-energy, in which case our universe is metaphysically necessary; (ii) The argument from quantum modal realism (cf. A. Wilson); (iii) the argument from L.A. Paul's one-category ontology; (iv) Gunn's argument for the fundamental constituents of matter as metaphysically necessary.
