Object cognition is a basic capacity shared by many creatures in the animal kingdom. Self-consciousness or self-awareness, by contrast, seems to be a rather advanced capacity that is enjoyed only by relatively fewer beings. It might thereby be assumed that many creatures can have the capacity for object cognition without any interesting capacity for self-awareness. In this essay, I argue that a certain capacity for object cognition - cognition with the engaged stance - requires the capacity for awareness of oneself as a physical object in an objective world. I further argue that some animals in the actual world do have the kind of capacity for object cognition in question. These two theses together yield the conclusion that those animals - such as human infants and some other non-linguistic mammals - actually have the capacity for awareness of oneself as a physical object in an objective world, contrary to appearance. I call this two-premiss argument the Object Cognition Argument, mirroring Quassim Cassam's Objectivity Argument (1997). Chapter 1 "Objectives" lays out the philosophical background and aims. Chapter 2 "Objects" discusses two capacities that underlie object cognition: object permanence, the understanding that things can persist when being occluded; and the constraint of solidity, the understanding that solid objects do not collocate in space at the same time. Chapter 3 "Objectivity" starts with object permanence and argues that it requires allocentric spatial representations, which further require awareness of oneself as a denizen of an objective world. Chapter 4 "Objecthood" starts with the constraint of solidity and argues that it requires representations of primary qualities that further require awareness of oneself as a physical object. Chapter 5 "Objections" modifies the Object Cognition Argument in light of three prominent objections: the Body Blindness, the Qua Subject, and the Missing Self Problems.