Omega Seamaster 30 ref.2639-8 (1950s) - originality check

Hi all,
first of all: I'm excited to see what the experts can tell me about the watch, let me say thanks in advance. I do appreciate it.

A short background to the watch:
It's already in my possession, but please feel free to be brutally honest. It's gonna be my family's gift to my dad for an upcoming, round birthday. He has never been into watches, but used to have a Seamaster similar to this one as his only watch for over two decades, mostly unaware it was a luxury product. It was stolen at some point, he'd never spend the money on another one (nor would he wear one as a gift it was too expensive), so when I was offered this one for ~450EUR I bought it. It might not be all original, the dial might have been repainted, etc., but I know my dad couldn't care less about all that. The movement starts right with the first spin of the crown, it holds time within half a minute / day, which I find exceptional for a vintage watch, and also I'd guess it's from the early 50s, just like him. As a present it should work quite well.

Nevertheless: I'm curious. I do like those vintage Seamasters and I could see myself wearing a similar one, maybe with a white/creme dial, so I started to look up the reference# and couldn't find a single one that looked just like "mine". There seem to be a few with the same reference 2639-8, but different movements, not the 265, but mostly I find watches with a different style of subdial (an "embedded" circle, in lack of a better term). To sum it up:

-Do you think the watch is genuine, especially since I cannot find another one like it? I'd also like to mention specifically that case back and plexi don't carry the Omega sign, which might be original nevertheless?
-Do you think the dial was repainted at some point?
-Is it possible to pinpoint the exact year of its production?

Thanks a lot, I'm excited!

I would also agree that the dial has been refinished. Swiss made print above the minute indices did not happen until the 70's I'm told.

Thanks a lot! That’s very interesting so far. Searching for the ref., what I find from Omega doesn’t match:

https://www.omegawatches.com/de/watch-omega-other-omega-ck-2639

This one, listed on Chrono, does match in size (36mm), caliber and case back (including ref):

[url]https://www.chrono24.de/omega/vintage-calatrava-herrenuhr-36mm-stahl---cal-265---1950--id12884574.htm?SETLANG=de_DE&SETCURR=EUR[/URL]

So the best guess would be that it’s a Calatrava that received a different dial with different indices and was painted black, I assume?