And I would not really expect to find an 1940's , still with the factory crystal , after 75 years.....
Weren't a good number of watch crystals in the 1940s made from some variant of clear celluloid? Hence why a lot of watches have yellowed, almost wrinkly crystals.
Is there a way to determine if the crystal is the "correct" one for this model? Or even determine if it's an Omega?
No.
However, with the age of the watch, if the crystal was original, I'd expect to see a lot of structural degradation, e.g. micro cracks in the plastic.