Help Identifying My Grandfather's Watch

Looking for some help identifying my Grandfather's vintage Omega. I was gifted it years ago shortly after he passed away, but don't know much about its origin. I believe he bought it either in Europe during WWII or shortly after he got back to the US in the mid-1940's. As you'll note, the minute hand has become detached and I'd like to get it repaired, but want to learn more about it first. Some interesting notes: (i) no "SWISS" or "SWISS MADE" on the dial (ii) unique crown, assume after-market (iii) no inscriptions on the back. Any information or insight would be much appreciated, thanks!!

Thanks! I am curious to see that as well. Will update when I bring it to a jeweler.