I'm working on a custom object and I have an Approval Process for this custom object.
I set the Entry Criteria for the Approval Process to be when Formula evaluates to True and set the formula to be True. In this way all records are allowed to edit the Approval Process
When the User is the owner of the Record then hitting "Submit for Approval" works fine
When the User is NOT the owner of the Record then hitting "Submit for Approval" returns the error message of No Applicable Process found.
I tried changing the Sharing Settings for the custom object to be Read/Write and that made no difference. They also have FLS giving them access to all the fields.
When a system administrator submits for approval it works fine.