I mean the search pages in itch.io site using tags and filter not Google. I guess that they don't require indexing because they work based on tags and setting information given in uploaded game. My game was shown by them well immeately after I uploaded my game.
My game page was not deleted nor recreated. I just tried to change the settings and information of my game project after I found that it was disappeared from the itch.io search by tag pages.