Mortimer Adler came to the Christian faith fairly late in life, and to the Catholic faith in particular, even later. Nevertheless, even before his conversion and throughout his professional career, Adler made no apologies for defending his belief in God (or a Supreme Being of some kind) based on the existence of a contingent universe. His own argument goes roughly like this:
1. If X is an effect in need of a sustaining cause Y, then the existence of X implies the existence and action of Y. (Premise)
2. The universe is an existing effect. (Premise)
3. The universe is radically contingent. (Premise)
4. Whatever is radically contingent requires a sustaining cause. (Premise, PSR)
5. Therefore, the universe has a sustaining cause. (From 1 - 4)
(1) and (2) are indubitably true. (3) seems fairly benign upon consideration. Adler distinguishes between radical contingency and superficial contingency, the former of which entails the possibility of one or more alternative states of affairs. For example, the universe as it presently exists could logically exist differently. The laws of nature could be different; my desk could be yellow instead of black; the Steelers could have beaten the Packers in the Super Bowl; and so forth.
(4) is Adler's interpretation of the Principle of Sufficient Reason (PSR). Instead of going into a defense of the PSR, it is worth considering a common objection. It is often alleged that these arguments commit a composition fallacy. Just because each part of a mountain is small, that doesn't mean the mountain as a whole is small. Likewise, it is thought, even though each part of the universe has a sustaining cause, that doesn't mean the universe as a whole has a sustaining cause.
The disparity in this analogy is evident whenever we try to apply causal explanations. Would it be wise to suggest that even though each part of the mountain has a causal explanation, the mountain as a whole does not? Surely the mountain itself has been formed by geological processes, etc. What this illustrates is that while there are cases in which the whole is not like its parts, there are other cases in which the whole is like its parts.
Adler then reasons that the sustaining cause of the universe must have the usual transcendent attributes of timelessness, immutability, and immateriality, in addition to enormous power.
It turns out that Adler's argument is pretty close to Leibniz's own formulation of the cosmological argument.