And according to Richard Barrow's interview, there's no time limit for Thailand Pass which implies that you may apply as early as you want to ensure you have the pass document.
By the way it's a great news for me to learn that only the result needs to be issued within 72 hours of departure, do you know if anyone did research on this rule? My flight will be on a Monday which I worry taking the test on the previous Friday won't be early enough since most of the testing locations don't work on Weekend. If only the result is needed to be within 72 hours then I may take the RT-PCR test earlier.