Help with 1950s Omega

Hi

I'm thinking of buying this watch, but have very limited knowledge on vintage Omega's (just really love the look of the watch).

The date inscription on the back of the case is in American date format and the watch has apparently been cased by Star watch company. Could I conclude the watch is one sold into the US by Omega? Should the movement not then h ave the "OXG" mark on it?

Do you think the watch is genuine? The advertiser says the watch has original factory dial and crystal too. Does it look and feel correct?

Thanks

Hi Dan. Where is the damage? Thanks

Thanks for pointing out

Besides the dial. Damage to the gold filled lugs. Main the bottom right inside tip and damage to another