I understand the confusion, it seems like it’s trying to prove a negative. I was confused about it myself when I first heard about it. GAE was never supposed to be falsifiable, it is (or should be) a question that science is unable to address, leaving room for a certain theistic interpretation of Genesis.
The claim being refuted is that science rules out all scenarios for a recent A&E; It doesn’t. There are people who have a barrier to accepting science (and evolution in particular) because they think it contradicts their religious beliefs. GAE is intended to poke a hole in that barrier.
Personally, I think GAE is unlikely in many real world scenarios. BUT if we already accept that A&E could have been recently created recently, then a little extra divine nudge to make that unlikely sequence of events pan out should be no big deal.