It's been decades since you could do that for yourself. It must be something like 20 years ago on Alta Vista that I got burned using search queries as bookmarks and (surprise, surprise) suddenly not being able to find "that page" any more.
I believe the issue OP is addressing is that even given an identical index, two different users might see to entirely different search results, as their individual search history is factored into the query.
You will see this giant network of the same site that tries to sell you on e-pdfs
You could try opening an incognito window, although it could still give different results based on geo location.
Or user agent, or screen resolution, or Accept-Encoding / Accept-Language headers, or installed fonts, or installed browser plugins detected, or Do Not Track settings.