The version of the modal cosmological argument (MCA) that I defend goes like this:
1. Every contingent entity possibly has an external cause. (Premise, W-PSR)
2. If the sum total of contingent entities C has an external cause, that cause is a necessary, eternal, and enormously powerful entity. (Premise)
3. C is a contingent entity. (Premise)
4. Possibly, C has an external cause. (From 1 and 3)
5. Therefore, the external cause of C is a necessary, eternal, and enormously powerful entity. (From 2, 4, and S5)
The argument is logically sound, but are its premises more likely true than their negations? Prima facie, almost nobody questions (1). Assuming it's possible for a brick to pop into existence uncaused out of nothing, it's still reasonable to conclude that the brick could have had an external cause of its existence.
(2) is largely analytical. If there is a cause outside the sum total of C that causes C, that cause must have necessary existence. Otherwise, it too would be contained within C. Moreover, this necessary entity would have to be eternal, since there is no time at which a necessary entity can fail to exist. Finally, the entity in question must also be enormously powerful, since a cause's power is at least as great as its effect. The sheer vastness and order of C warrants this conclusion.
Notice what the skeptic cannot argue. He cannot start by reversing the W-PSR:
1*. Every contingent entity possibly does not have an external cause.
The existence of a necessary, eternal, and enormously powerful entity is consistent with its not having caused what exists contingently. What the skeptic would have to do is begin by saying that a necessary entity possibly does not exist. However, this possibility premise entails the much stronger conclusion that C cannot possibly have an external cause. This brings the original W-PSR back into question. So, the skeptic will have to pick their poison.
At any rate, I could argue that a necessary entity's possible non-existence is contradictory (and I think it is), but for now, it's important to realize that not all contradictions are as immediately obvious as the next. "The Prime Minister is a prime number" is necessarily false, but it's nowhere near as obvious as, "X is ~X."