Since Itch does not talk about such things, do not expect an answer from support or an admin. The community message board moderator is not the kind of moderator the faq talks about.
If there is a threshold, it probably is the checkmark icon you see on some accounts. See the top page of https://itch.io/games/top-rated . But you will notice that there are games with many thousand ratings, that still do not have that verified account sign. Itch just does not verify all that many accounts. And frankly, they cannot afford to protect even those accounts from the mechanisms that puts some new games and updated games on the waiting list. After all, there are reasons when the system wants staff to have a look. Itch does intentionally not tell what those reasons are, but they obviously exist.
And to clarify, I am pretty sure the faq only talks about the situation when a game gets put on the list, because it is a first time paid game. There are plenty other reasons why a new game or an updated game might end up on that waiting list. The problems only arise, since indexing takes weeks and not days - if you have to wait.
That waiting list is not first in first out. Games with more traffic are supposed to have higher priority. But think about it. Your game is not the only one on that list with a similar traffic, and there are bound to be a lot of games with more traffic.
My opinion, based on some threads I read, is that Itch's opinion about indexing is, that it is a bonus and not essential. After all, a page is fully functional, with or without indexing and if you do promotion, you are promoting a direct link to the game or at least your account and do not say, hey target audience, head to Itch and search my new game by name.
Also, search does not even work on the Itch app. So there is that.