Persona 5 Royal

You need to wait until you can start officially exploring Mementos to be able to collect stamps, which starts in the Path of Aiyatsbus. While exploring, there is a random chance of finding Jose on each floor, and the first time you interact with him he will explain how stamps and flowers work. You'll get this the first time you trade stamps and unlock one stage of a Mementos cognitive change line.

There are 8 stamps in total in Aiyatsbus (and 2 now will appear on the previous floor, so don't forget to backtrack and get those!). Some stamps are in fixed locations (like just before the exit of every floor) while others are randomized. See below for a list of stamps per path:

Path: Stamps
Qimranut: 2
Aiyatsbus: 8
Chemdah: 10
Kaitul: 20
Akzeriyyuth: 25
Adyeshach: 30
Sheriruth: 30
Iweleth: none
Da’at: 40