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If you watch does not have a calendar date, then it is likely a "frankenwatch", cobbled together from parts of other watches.
From the Omega Vintage Site:
Caliber number: 504
Created in 1957
?de luxe? - luminous (radium) - with hand-riveted, facetted gold hour markers and gold hands
MORE PRODUCT INFORMATIONS
Case: round (35 mm)
press-on case back with " O-ring " gasket.
Watch reference : 2943 (also existing in 14K yellow goldcap, 14K or 18K solid yellow gold)
for leather straps of 18mm lug-size
International Collection: 1975-1962
Price: not available
Hope this helps,