An acceptance of the PSR leads one to believe that the whole of contingent reality C has an explanation of its existence. Now, an explanation can be of one of two types: a thing's explanation is found either in the necessity of its own nature or in an external cause. Since C does not exist by a necessity of its own nature, it follows that C's explanation is found in an external cause. This external cause must be a necessary and eternal entity N, as well as very powerful in order to cause something as vast as C.
Let's suppose the atheist not only denies that N is God, but that there is any such entity as N. The atheist could do this, for example, by denying the PSR. The problem is that this presents the atheist with a new challenge. For, design arguments often present the uniformity of nature or the fine-tuning of the universe's initial conditions within the context of a trilemma:
1. The laws of nature are either due to necessity, chance, or design. (Premise)
One would be hard-pressed to think of a fourth alternative to premise (1). Keeping in mind the atheist's denial of the argument from contingency, especially the existence of N, we are led to premise (2):
2. The laws of nature are not due to necessity or chance. (Premise)
From these two premises, it follows that:
3. Therefore, the laws of nature are due to design. (From 1 and 2)
But surely the atheist does not want to affirm (3)! Yet, he already denies one of his alternatives, which leaves him with only one option: the affirmation that the laws of nature (and/or the universe's fine-tuning) are due exclusively to chance. Remember, there is no N at all according to this radical position, so the laws of nature cannot be the products of a combination of necessity and chance.
Obviously, if the chance hypothesis doesn't pan out (and there are good reasons to think it doesn't), one must accept that N exists and/or that the laws of nature are designed. Whichever route is taken, a large chunk of either the contingency or design arguments must be affirmed as a matter of consistency.