What I gained from your situation is the product is source inspected before packaging and then the sealed cartons sit, typically for weeks, before shipped. It has not been determined how or when FOD is introduced to the parts. [In case any reader doesn't know the acronym, FOD is Foreign Object Debris.]
One measure that could provide answers is to conduct what we used to call a Dock Audit. Randomly sample a final-goods package out of the warehouse, open the box and inspect the condition of its contents, the morning before the product is shipped. This special one-time audit is conducted by an internal auditor or senior quality staff of the supplier, or it could be a customer auditor, or it could be done by a third-party auditor depending on criticality and what your budget might be. After the auditor documents the contents and condition, the contents are re-packaged by operations workers and sealed. Then, if desired, the same package can be audited and compared upon arrival and opened on the customer's dock.