One can run a minimal modal ontological argument for naturalism with just two simple premises:
1. Possibly, a necessarily existent natural universe exists.
2. What's necessary doesn't vary from possible world to possible world.
3. Therefore, there is a necessarily existent natural universe.
(2) follows from Axiom S5 of S5 modal logic, and most philosophers accept S5, so it's fairly uncontroversial. So the argument comes down to the plausibility of (1).
But (1) is plausible as well. For the most plausible interpretation of quantum mechanics is arguably the Everettian interpretation, and as Alastair Wilson has recently argued, one can provide a plausible naturalistic account of modality in terms of Everettian quantum mechanics, which he dubs quantum modal realism (QMR). Roughly: a possible world is a branch of the universal wave function; something is possible just in case it exists in at least one branch of the wave function; and something is necessary just in case it exists in every branch of the wave function. Finally, because the empirical evidence underdetermines whether the decohering branches of the wave function share an initial segment (the overlapping interpretation) or have qualitatively identical yet numerically distinct initial segments (the diverging interpretation), de re modality can be spelled out either in terms of transworld identity (which corresponds to the overlapping interpretation) or in terms of counterpart theory, according to which individuals are worldbound (which corresponds to the diverging interpretation). So in light of the machinery of QMR, (1) asserts that it is true within at least one branch of the wavefunction that the natural universe exists in every branch of the wave function (which is true in our branch, and of course in every branch), where the de re modal properties of the natural universe are given either an overlapping, transworld identity gloss or a diverging, worldbound/counterpart-theoretic gloss.
Furthermore, (1) seems more plausible than the theistic possibility premise in the corresponding modal ontological argument for theism. For the truth of the latter premise requires acceptance of the compossibility of a large swath of exotic properties, such as omnipotence, omniscience, moral perfection, immateriality, and the capacity for creating individuals and/or stuffs out of nothing. Therefore, it appears that one has more reason to accept the minimal modal ontological argument for naturalism than the standard modal ontological argument for theism.