Good point with the google. Who markets with, hey I have a game on itch, go there and use their search button. I would imagine you would market the direct link, especially in an online article. It is not even a deep link, it is just a combo of username and game page. But on the other hand, direct links is exactly how scammers "market" stuff (by spamming). Tbh, the game in question is not a game whose name I would be able to put into a search engine without copy/paste...
I think a disclaimer at the relevant portion of the uploading site would solve this. Because, even if there were a button, you only come into this situaion if you unknowingly think that uploading first time paying game will be listed as soon as you upload it and can thus control the timing. The button would have to explain the situation - making the button obsolete.
Oh, btw, the game is listed now.