Final answer:
Object permanence develops during Piaget's sensorimotor stage, between 5 and 8 months of age, as infants learn that objects still exist even when not directly visible.
Step-by-step explanation:
Object permanence is a critical developmental milestone in Jean Piaget's theory of cognitive development. According to his theory, object permanence is developed during the sensorimotor stage, which spans from birth to about 2 years of age. In the sensorimotor stage, infants learn about the world through their senses and actions, including motor behaviors like grasping and looking. Between 5 and 8 months old, infants start to understand that objects continue to exist even when they are out of sight, manifesting the ability of object permanence. This concept is essential for an infant's growing awareness of the world and the development of memory and comprehension.