If I cannot verify the individual watch's serial, I would usually pause the purchase. A serial is not the whole provenance story, but losing that identifier makes theft screening and document matching less reliable.
There can be an innocent explanation
Some serials are hidden by a bracelet, hard to photograph, or faint on an older watch. That is different from a seller refusing any safe inspection or presenting an engraving that appears altered.
Ask for a safe, independent check
A qualified watchmaker may be able to inspect the serial without disassembly or damage. Ask the seller to meet at an established shop and agree in writing who pays. Do not remove a caseback or bracelet yourself unless you are qualified.
Make the decision conditional
If the serial remains unreadable, consider walking away. If you proceed despite that limitation, understand that a database search may not be possible and use stronger provenance, seller, return, and payment protections. No workaround removes the uncertainty.
Pressure to pay before inspection is a reason to stop. A legitimate seller should be able to explain the limitation and allow reasonable verification.
Find the Serial Safely
Use model-specific guidance or a qualified watchmaker before entering an identifier.