According to L.A. Paul's one-category ontology, there is just one kind of thing: qualities (i.e., properties). Qualities are universals -- i.e., repeatable entities -- that (arguably) exist necessarily and a se, and have a nature closer to Aristotle's immanent (non-substantial) forms than Plato's transcendent forms (there are no uninstantiated qualities). All the rest of reality is ultimately explained in terms of mereological fusions of n-adic qualities. The fusion relation is a composition relation, and so derivative entities are composed of basic qualities. The resultant picture is mereological bundle theory:
On my view, matter, concrete objects, abstract objects, and perhaps even spacetime are constructed from mereological fusions of qualities, so the world is simply a vast mixture of qualities, including polyadic properties (i.e., relations). This means that everything there is, including concrete objects like persons or stars, is a quality, a qualitative fusion, or a portion of the extended qualitative fusion that is the world-whole. I call my view mereological bundle theory. (Paul, "A One Category Ontology", p. 2)
According to mereological bundle theory, the world (here, I need not confine myself to the physical world, so by ‘‘world’’ I mean the whole world, not just the cosmos) is a vast mixture of properties, some with a single location (whether in configuration space, or in spacetime, or in something else), some with many locations, some located everywhere, and perhaps even some without any location at all (Locations are defined by n-adic properties. For simplicity, take the fundamental space to be relational, and define up ‘‘points’’ in the space using these relations and properties). The world is constructed from arrangements of properties and relations that are fused together to make things of all sorts: concrete objects, abstract objects, events, states of affairs, facts, fields, regions, and anything else there is. So, according to the mereological bundle theorist, fields, particles, entangled systems of particles, spaces, molecules, cells, bodies, persons and societies are all constructed, most fundamentally, from fusions of properties and relations. (Paul, "Building the World From Its Fundamental Constituents", p. 242).
Paul's one category ontology provides a nice an ontological framework for contemporary physics:
...consider the wave-function realist who takes the world-whole to be a wavefunction. On the GRW theory of the world, the world is a universal wave function that evolves in accordance with the dynamical laws. Understood in terms of mereological bundle theory, the wavefunction is the fusion of amplitude and phase properties (along with any other properties of the system) with structuring properties or relations, including the structuring relations described by Schrodinger’s equation and by the collapse postulate. A variant of this view can fit the Everettian approach, and one can also fit David Albert’s (1996) treatment of Bohmian mechanics by adding a world-particle that is simply a fusion of properties to the plurality of things. (Ibid., p. 254).
I think a naturalist who adopts Paul's one-category ontology can exploit her account to explain the existence and fine-tuning of our universe. To start, consider that if we assume with Paul that the world-whole is just the sum of all qualities, and they can combine in various ways in accordance with the constraints of their intrinsic natures, what prevents them from combining in every possible such way? It would be mysterious why they fuse/bundle in some ways and not others if they didn't fuse/bundle in every way consistent with their natures. Paul's one-category ontology thus naturally generates pressure to accept a mereology-focused variant of Spinoza's negative PSR:
Negative Mereological PSR (NMPSR): a given plurality of qualities will fuse/bundle unless there is a sufficient reason for why they do not.
Given NMPSR, then, we should assume that all possible bundles/fusions exist in the world-whole. If so, then we can explain everything the theist wants explained:
Why does anything exist? Because qualities exist and they're necessary beings that exist a se.
Why does a universe exist? Because (as we know from our observations of the actual world) there is a compossible distribution of qualities in some "region" of the world-whole that comprises a universe. So by that fact and NMPSR, there is a presumption to think that it is inevitable that there is a fusion/bundle of those properties -- i.e., a mereological fusion of qualities that make up a configuration space, along with a fusion of phase and amplitude properties, that compose a universal wavefunction. From non-spatiotemporal property configurations like this, you necessarily get spatiotemporal universes that logically supervene upon them.
Why does this universe exist? By NMPSR, absent a good reason to think otherwise, we should assume all possible universe quality fusions exist inevitably and necessarily within the world-whole of qualities, and this is one of them.
 On Paul's account, the relation of mereological bundling here is not a fundamentally spatiotemporal one of spatiotemporal parts composing a spatiotemporal whole. This is because contemporary physics seems to have shown that spacetime isn't fundamental (think, for example, of wave function realism with respect to quantum mechanics, theories of quantum gravity that take spacetime to be emergent, etc.).
 Question: How does a quality become spatiotemporally localized on Paul's view? Answer: By bundling with spatiotemporal properties/relations: "Objects may have their locations in virtue of being fused with whatever location properties and relations there are that define the actual space of the world, and many objects will have a physical structure in virtue of having location properties and relations as parts of their fusions, or in virtue of being part of a larger fusion which has location properties and relations as parts. The character of the space might not be what we take the character of ordinary spacetime to be, but the structure of the space is generated by fusing qualitative properties with relevant properties and relations that define the space as determined by modern physics. Hence, the view is consistent with (and explicitly accommodating of) various approaches in modern physics: it is friendly to structuralism, and is perfectly consistent with realist interpretations of the ontology of quantum mechanics, for example, with realism about the wavefunction." (Paul, Building the World From Its Fundamental Constituents", p. 242).
 As Paul points out, her one-category ontology is compatible with a parts-to-whole mosaic, as well as a holistic whole-to-parts picture. She prefers the latter because it's a better fit with with quantum holism/entanglement phenomena.
 We might not even have to appeal to NMPSR here. For there are good grounds for thinking Everettian QM (EQM) is true, and as Alastair Wilson points out, EQM allows for different fundamental parameters within the universal wavefunction (indeed, it allows for all possible parameter variations). If so, then (given this fact plus the decoherence mechanism of EQM) EQM can generate something akin to a level-5 multiverse, where every possible universe exists in some branch or other of the universal wavefunction.