I feel like they took off with https://en.wikipedia.org/wiki/Cow_Clicker , which was a satire that people unironically found hugely enjoyable. But that was much later in 2010. Everything has to start somewhere; maybe Progress Quest was the first idle game?
Cow Clicker and Cookie Clicker are not idle games. You have to interact with them constantly and the less you do the slower you progress.
Idlerpg for IRC is the opposite. If you act you are punished.
Progress Quest is totally idle. It has a bunch of internals that just increment numbers and pretend things happen. It’s an app you start and then don’t do anything at all with.
All the clicker games, and the weird unfolding games like A Dark Room, Candy Box, Paperclips, are kinda fun but not in the spirit of Progress Quest.
I'm not sure how much to trust the Wikipedia dates for these - it claims Cookie Clicker was 2013, but I'm sure there was a flash version of it before 2007, while I was in highschool.