A common (Humean) tactic is to assume the PSR for the sake of argument, while simultaneously denying the soundness of the cosmological argument for a necessary entity by postulating an infinite regress of contingent causes. As long as each contingent entity is caused by another contingent entity, then the whole is explained by the existence of its parts, and that's it. No further explanation for the whole is needed.
There are several ways to counter this objection. One is to offer arguments against an infinite regress of causes, whether they be originating causes or sustaining causes. Another route, championed by Samuel Clarke and more recently defended by atheistic philosopher, William Rowe, is to point out that the series of contingent entities itself need not exist. Even if there is an infinite regress of contingent causes, that infinite regress itself exists only contingently.
This can be further illustrated by an analogy inspired by Alexander Pruss. Imagine a set of acorns and oak trees that extends infinitely into the past. Oak tree 1 is caused by acorn 1, acorn 1 is caused by oak tree 2, oak tree 2 is caused by acorn 2, and so forth. The set of oak trees is caused by the set of acorns, and the set of acorns is caused by the set of oak trees. This, of course, is circular, and does not explain why there is a set of acorns and oak trees at all. Unless one asserts that the set has necessary existence, then by definition the set exists contingently and therefore stands in need of an external cause.