Object permanence is linked to separation anxiety and starts at 6-8 months and becomes permanent at 16-18 months. It is a period of rapid cognitive development.

In the first year, Babies discover everything has a life of its own even if it is out of sight. Objects appear to disappear and reappear.

https://www.simplypsychology.org/sensorimotor.html

Infancy is characterized by extreme egocentrism, where the child has no understanding of the world other than their own current point of view. The main development during this stage is the understanding that objects exist and events occur in the world independently of one’s own actions (‘the object concept’, or ‘object permanence’).

Object permanence means knowing that an object still exists, even if it is hidden. It requires the ability to form a mental representation of the object.
For example, if you place a toy under a blanket, the child who has achieved object permanence knows it is there and can actively seek it. At the beginning of this stage the child behaves as if the toy had simply disappeared. The attainment of object permanence generally signals the transition to the next stage of development (preoperational).

The 6 stages of object permanence

https://wehavekids.com/parenting/The-Six-Stages-of-Object-Permanence

How it relates to separation anxiety 

Separation anxiety and the toddler who clings to you like a koala

Separation Anxiety and its’ effects on baby sleep