There have always been pirates, from prehistory until the present day, including the periods between the more romanticized times of Drake, Morgan and the time following the War of Spanish Succession. I think the broadest definition I've seen for the GAoP is something like 1560 - 1730 which fairly well covers everything. Well of course unless you want to count those pirates who came before and after.
Kidd is mostly remembered because he had a catchy name and he wound up being a political pawn. Tew is not someone most in the general public have ever heard of. I read of a study where people were, at random, ask to name a pirate. Something like 95% of them named someone active between 1714 and 1722 and my guess is most of the other 5% named Morgan.
Avery is an interesting character though. Avery's career spans that period just prior to the beginning of the War of Spanish Succession (1701) making him the stuff of legend while such GAoP pirates as Teach, Vane, etc were young. You could make a case that he was the father of the GAoP, but the big explosion in piracy still occurs following Queen Ann's War and fairly well dies out, on a grand scale, following the death of Bartholomew Roberts.
When I look at these periods I look for a preponderance of activity which is why I have gravitated toward the definition I proposed. Of course there are many who have other definitions so it would appear that there is really no generally agreed upon definition of what constitutes the Golden Age of Piracy leaving it to the student of the period to decide on his or her own definition based on what their studies indicate is relevant.