OWD of an object is set as private. Manager with role does not have read access to the object.How to open up records of the object to the manager?
You can add the manager to a public group and create criteria-based or role- based sharing rules on the object to share records with the public group.
This is assuming she has object level read permission. Your question says without read permission on object but the problem sounds like the manager doesn't have record level access.
Permission sets and profiles handle object CRED perms, while owd and sharing handles record access. So you may also need to great R on tbe object via a permission set.
There is a video series called "who sees what" that is quite good at explaining this.