A serial can disprove authenticity but never establish it. If the number dates to before the reference existed, if it contradicts the caliber inside the case, or if it is shallowly etched rather than crisply engraved, you are looking at a counterfeit or a re-cased watch. The reverse never holds: a plausible serial is exactly what a good fake carries, because it was copied from a genuine watch.
For an authoritative answer, Omega sells an Extract from the Archives, which returns the caliber, reference, production date, and original delivery destination for a specific movement serial. It is ordered through Omega directly and is the document serious vintage buyers ask for. Our 11-point authenticity checklist covers the physical tells, and the serial number location guide shows where every major brand hides its number.
Before buying, run the serial against The Watch Register and Chrono24's stolen-watch database. Both are free to search and both cover serials reported stolen.