Simply put: no, it's expected that they will not have a 529. A 529 is for paying current qualified expenses, "current" in this context meaning within the same calendar year. If you graduated this past May, you possibly have qualified expenses that you paid earlier this year that can be reimbursed from your 529 THIS YEAR, even if those expenses were paid with loans. Take a distribution and pay off some of your loans, if you have qualified expenses that were paid this year. For qualified expenses that were paid in previous years, it's too late to use the 529 without taking the hit on taxes and the 10% penalty on the earnings part of any distribution.
Why is it that you have a "growing 529 balance" if you just graduated? This is not a normal situation, unless you are attending or planning to attend graduate school, and then of course you can use the 529 account for graduate school expenses. But most people who have a 529 begin funding it well before the beneficiary goes to college, and then spend the money down through the college years, so that any necessary loans are taken after the 529 has been exhausted.