Thought experiment: let's say that anonymity was such an important thing to the average Google user that they would decide to use alternatives if they felt that

Thought experiment: let's say that anonymity was such an important thing to the average Google user that they would decide to use alternatives if they felt that their anonymity outside of their Google account was being compromised. Could Google know enough information about you to correlate data over a lot of your activities and preferences, but still make it so that you yourself are anonymous to them and the outside world (with a high degree of certainty)? If we are not their products, then do they really need to know enough information about us to actually make a profile that is matched to our real identities? Obvious problems are, for example if they know enough stats about your physical description to pinpoint you pretty accurately, and they also know where you live, and there are only 10 other people that live in that place. Even if they don't actively try to deduce your identity, it is very easy to do so with the available information.