(Revised a bit more in light of J.D.'s helpful comments)
As I mentioned in a previous post, it's commonly thought that a naturalist can't plausibly accept the Principle of Sufficient Reason (PSR), on the grounds that (i) she thereby commits herself to the existence of a metaphysically necessary being (more carefully, a metaphysically necessary concrete object), and that (ii) this is incompatible with any plausible version of naturalism. In the previous post, I offered reasons to doubt (i). Here I'll briefly argue that (ii) is doubtful as well. As before, I'll use some remarks from William Lane Craig as my foil.
As a part of his defense of the Leibnizian cosmological argument, Craig has argued that the universe cannot plausibly be considered a metaphysically necessary being. He offers three main lines of argument for this conclusion: (1) our modal intuitions indicate that there could've been no universe at all, which is evidence that our universe isn't metaphysically necessary; (2) our modal intuitions indicate that there could've been a different universe, composed of different quarks, which is evidence that the universe isn't metaphysically necessary; and (3) there are good scientific arguments (esp. the ones in support of the Borde-Guth-Vilenkin theorem) and philosophical arguments (viz., Craig's arguments against the existence and traversability of actual infinites) that the universe had an absolute beginning, which is evidence that our universe isn't metaphysically necessary. I find Craig's type-(3) arguments unpersuasive, for reasons I've discussed on other occasions. I will therefore ignore them here and focus on (1) and (2).
Start with (1): our modal intuitions indicate that there could've been no universe at all, which is evidence that our universe isn't metaphysically necessary. In support of this claim, Craig appeals to Charles Taliaferro's account of justification-conferring inferences from conceivability to possibility: "If one can conceive that a state of affairs obtain, and one has carefully considered whether the state of affairs is internally consistent (self-consistent at a minimum) and consistent with what one justifiably believes, then one has prima facie reason to believe it is possible for the state of affairs to obtain." Therefore, if this account captures a correct principle of justified modal inference, then if you can conceive of the non-existence of the universe in this way (i.e., on reflection you find no internal inconsistency in the idea, and you find the idea to be consistent with what you justifiedly believe), then you thereby have prima facie reason to think the universe's non-existence is metaphysically possible. And if that's right, you have prima facie reason to think the universe is not a metaphysically necessary being.
What to make of this argument? Let's grant that we can conceive of the non-existence of the universe in the way sketched above. The concern is not with that step of Craig's argument, but rather with Craig's recommended principle of justified modal inference. Here I will just say that even if Craig's has identified a correct principle of justified modal inference, it's a dialectically ineffective tool if offered to the atheist or agnostic in the context of Craig's defense of the Leibnizian cosmological argument. To see this, consider a reflective agnostic who can conceive of God's non-existence as well. So, for example, she coherently conceives of eternal, uncreated, existentially independent matter in a godless universe. Furthermore, she finds that this conception remains intelligible to her after careful evaluation of its internal consistency, and of its consistency with the other things she justifiedly believes. Therefore, on Craig's recommended account of justifified modal inference, she has prima facie reason to believe that God's non-existence is likewise metaphysically possible.
Let's look at (2), then: our modal intuitions indicate that there could've been a different universe composed of different quarks (or with more quarks or less), which is evidence that the universe isn't metaphysically necessary. Now we've seen that Craig's preferred account of justified conceivability-possibility inferences is dialectally ineffective (at least in the present context). However, let's grant that even without an adequate account of justified modal inference in hand, we have a good deal of justified modal beliefs. Suppose we further grant that the possible existence of a universe composed of different quarks (or with more quarks or less) is among them. The problem is that we have similar modal intuitions about God: Assume the triune God of Christian theism exists. Why this God, instead of, say, a non-trinitarian God (e.g., the God of Islam)? Pending an adequate criterion of modal inference, this line of reasoning is a problem for the metaphysical necessity of both God and the universe if it's a problem for either one.
Beyond this, one could argue that much of the plausibility of the reasoning in (2) turns on the assumption that our universe is the only one there is. For if instead we live in a multiverse that contains all possible universes -- where all possible kinds, quantities, and configurations of quarks exist --, then much of the puzzlement about the universe's seeming particularity evaporates.
One might reply that there is a remaining puzzlement about why the multiverse exists at all, but we've seen that the same applies to God. We've further seen that Craig's preferred criterion of justified modal inference can't help us adjudicate between the modal status of the two broad hypotheses here (God and the material universe). It therefore seems that we are still in need of a reason to think that God, but not the universe, is a suitable candidate for a metaphysically necessary being.
 "The Cosmological Argument", in Copan, Paul and Moser, Paul. The Rationality of Theism (Routldege, 2003), p. 130, fn. 8. Cf. Taliaferro, Charles. "Sensibility and Possibilia: A Defense of Thought Experiments", Philosophia Christi 3, 2 (new series) (2001), pp. 403-420. The account is given on p. 407. It should be noted that Craig endorses a slightly modified version of Talieferro's account, as he has removed the requirement that one form a mental image or visualization of the referent of a given thought experiment. I've read Craig's remarks in another venue that seem to indicate that this is intentional; he seems to reject imagination-based accounts of modal epistemology.
 One might attempt to get around these criticisms by offering a cogent ontological argument. If one could do that, then one could successfully argue that while the universe's non-existence is conceivable, God's is not. But if one had such an argument in hand, the Leibnizian cosmological argument would be superfluous. In any case, the ontological argument itself relies on an inference from conceivability to possibility, just as the cosmological argument under consideration here. Unfortunately, though, Craig's recommended criterion of modal inference seems to be just as dialectically ineffective in this context as it is in the context of the cosmological argument.
To see this, let's return to our reflective agnostic and follow along with her as she applies Craig's recommended criterion of modal inference to the key premise of the modal ontological argument (viz., that a necessarily existent Anselmian being is metaphysically possible). Thus, she finds no incoherence in the concept of an eternal, uncreated, free-standing universe devoid of a god. Furthermore, she finds no inconsistency between this concept and her other beliefs. So if Craig's recommended criterion of justified modal inference is correct, it follows that she has prima facie reason to think it's metaphysically possible for the scenario to obtain.
On the other hand, she also finds no internal incoherence in the concept of a necessarily existent Anselmian being, and she sees no inconsistency between this concept and her other beliefs (at least sans her newly acquired beliefs above. If we add those beliefs, then by Craig's criterion of modal inference, the claim that an Anselmian being is metaphysically possible is inconsistent with her other beliefs, in which case the latter is thereby defeated(!). But let's waive this problem here.) So if Craig's recommended criterion of justified modal inference is correct, it follows that she has prima facie reason to think it's metaphysically possible for the scenario to obtain.
Here's the thing, though: Our reflective agnostic of course also sees that the two beliefs are mutually inconsistent -- they can't both be true. For if a godless universe is metaphysically possible, then there is a metaphysically possible world at which God does not exist, in which case a necessary being is impossible (and the key premise of the modal ontological argument is false). On the other hand, if a necessarily existent Anselmian being is metaphysically possible, then an an Anselmian being exists in all metaphysically possible worlds, in which case a godless universe is metaphysically impossible (and the key premise of the modal ontological argument is true).
Thus, after reflecting on all of this, our agnostic finds that her prima facie reasons for believing each of the two modal propositions (i.e., that a godless universe is metaphysically possible, and that a metaphysically necessary Anselmian being is metaphysically possible) are undercut. She therefore finds herself undecided about the metaphysical possibility of an Anselmian being, and thus undecided on the key premise of the modal ontological argument. As with the cosmological argument, then, Craig's criterion of justified modal inference is of no help in vindicating God as a metaphysically necessary being via the ontological argument.
(I've offered a sketch of more general critique of the use of modal epistemology to vindicate the modal ontological argument on another occasion.)
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