As a Cat Sitter, I respect a cat’s space. 
The first visit I sit in the room they are in and just be quiet. Usually, a bedroom.
I sit on the floor and read a book while playing with a toy.  It is gratifying when I see a little paw reach out from under the bed to bat at the toy. 

Ah, Cat Sitter high! Next visit they will be more comfortable. They know someone who cares is there to take care of all of their needs.