Define "as quickly as possible". How long after the fact can Niantic tell that I was at Burger King for lunch?
If the answer is anything more than a week, I don't think they are really trying. Pokemon Go does need to keep some data longer because it's used in-game: when and where you caught a Pokemon that you still have; whether you have ever visited a given Pokestop (but not when); how long you've had Pokemon in a given gym. But the game never needs to save actual paths you followed.