AQA replied: "There's no average length of time, it just depends on the number of vacancies and the response. AQA advises applying immediately when they're advertised."
Now, call me a pedant, but I don't believe it's technically true that there's "no average length of time". I can entirely believe that they don't set a maximum or minimum length of time, and/or that they just don't want to tell me, but that's an entirely different kettle of question marks.