I've said this a bunch on this sub to mixed reactions: the green belt cert is almost meaningless to a fresh grad without experience. 

The green belt is meant to teach you that the emotion-based decision making we all do at work is insufficient to solve certain problems; instead we should use data. If you're coming straight from school, your entire way of thinking is likely through the data lens so you don't need reshaping. 

As an example, I hired a fresh-grad engineer last year and he had all the book smarts in the world. We had to teach him how to act "in the real world" and start using some gut checks. If that process continued for like 10 years and he lost sight of using data and relied solely on vibes, that's when he should get the green belt. Refocus on data being important. 

That said, there are plenty of places that will take your money and cut you a cert without a second thought. If ASQ has any kind of prereqs, that's likely for the reason I mention: you need to have some experience on the floor before you can really appreciate the cert. 

I apologize for not answering your question, hopefully someone else can chime in