Obtaining original papers and box

Unfortunately, the only way to obtain the original papers is at the time of purchase. At one time, Omega provided a certificate with information from their archives for a fee, but that service has ended.

As for the box, if you have a specific watch you are asking about, please post comprehensive photos and information. Or use the search function to find the many previous threads about boxes.

Honestly if the watch is not a rare historical model, the box and papers are pretty worthless unless the watch is high level collector or museum level quality. Watches where meant to be worn and replaced every few years. Box and papers is Rolex affectation, and even they have pretty much dropped it.

If papers are together with full set and they include original purchase receipt etc it is nice to see provenance and proof of one owner watch, but as @Foorama explained most collectors won’t pay a big premium for such. It’s hit or miss if owner kept the box and paperwork,
Some sellers fabricate this with papers from a similar but different watch, and pair with a vintage box which may or may not be correct. Of course these are only worth the value of the box ( usually not much) and that’s it.
While there are some boxes that were specific for certain watches and may be inscribed as such (Constellation, Seamaster etc) often the box was a point of sale pairing made by dealer so hard to pinpoint other than period correct.
If you’re into boxes search for Omega Box thread there are many pages to read.