If you truly believe governments don't care about search data or that the collection is benign, go ahead and log into Google (or use incognito. Probably won't make any difference) and start searching for things like child pornography, how to make pipe bombs, how to convert your guns to full auto, how to build a suppressor at home, how to make a deadly gas bomb, where to find a hitman, how to murder your wife without leaving evidence, etc. Get creative.
I imagine Google filters the bad stuff, so you're not likely to actually see anything life scarring with that first search. But go ahead and run the experiment and see if anything comes of it.