1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise)
2. If the sum total of contingent entities C has an explanation of its existence, that explanation is a necessary, eternal and very powerful entity N. (Premise)
3. C exists. (Premise)
4. Hence, C has an explanation of its existence. (From 1 and 3)
5. Therefore, the explanation of C is N. (From 2 and 4)
Let's assume the skeptic accepts premise (1), the Principle of Sufficient Reason (PSR). Instead, he objects that premise (2) commits a composition fallacy: if every contingent entity is explained by another contingent entity, ad infinitum, then C has a sufficient explanation.
I think the problem with this objection is that the regress of contingent causes is itself contingent; there didn't have to be any regress, finite or infinite, of contingent causes. If every part of a mountain can not-exist, then it's only reasonable to infer that the mountain as a whole can not-exist. Likewise, if every contingent cause can not-exist, then C as a whole can not-exist. If the skeptic wishes to deny this, then he is required to say that C is necessary, which is self-contradictory.