Not exactly, and it depends how memory is defined. If it's just the storing of information, then the universe has been doing that since it existed. Except that that just shifts defining memory, to defining the storage of information. And to defining information. Information itself appears to depend on the level of detail--humans ignore a vast amount of information when perceiving the world, for instance. If we consider ourselves as information-storage devices, we don't get to store all that much, compared to the much larger set of events; we appear to be adapted to a certain level of information input. Which seems to be the case for any physical device.