I estimate that it's 4 - 6 weeks.
I doubt we'll ever know what parameters the Airbnb search used and when you think about it, this is a good thing. If the information was available, there would be so many hosts who would game the system and not all of those hosts would be the scrupulous ones.
I also suspect that the teckies tweak the search facility very often so if we cracked it today, it might well be different tomorrow.
Just my opinion but I do think that it's better for hosts not to rely on the Airbnb search because who knows? There are SO many listings these days and new hosts who are getting the boost but if someone is searching for your exact parameters (for example, certain dates + pet friendly + number of guests + whole place or room + location + superhost + instant book + anything else you can think of, then they'll find you.)
This is a good thing because it means that we are getting views and inquiries mainly from people who are looking for exactly our type of rental. (Fewer time wasters!)
However, I still think that hosts shouldn't rely on the search system and promote their listings themselves.