Help identifying vintage Omega (1920-30s)

Hello guys!
I found my great-grandfathers watch and I'd like to renovate it. But first things first I need some help identifying what is this model and caliber.
It's a winding watch without seconds hand, that greatgranpa most likely got in interbellum, looking at series number (6877411) it checks out (1923-1930 for 6000000 series).
Here are some photos of the watch:
Thanks for help in advance!

Hello,
The case is not original Omega, the dial also isn't or has been repainted.
Caliber is a genuine Omega, looks like a 23.7 T2, serial dates its production from the end of the twenties.

Hey,
Thanks for answer and identifying caliber. I'd like to add that it's still working accurately.

I couldn't find any dial exactly like this one, but its print quality seem really good (although watch has been flooded) and numerals font closely resembles one used on some other models. Also, while I can't be 100% sure, I doubt anyone in my family changed the dial from original. Here is another angle showing that numerals are gilded:

Also watch hands have blue tint to them.
Giving a watch closer inspection I noticed some markings on the inside of back cover:

What else I can add it was bought in Poland.

At this point I'm wondering if case or dial can come from any different Omega model? And if it's cal. 23.7 T2, then it should have sub seconds mechanism, yes?

Hello,
The case doesn't look like any Omega production of whatever period. Is it signed inside the caseback? If it was an Omega production, it would be signed.
Regarding the dial, the logo is incorrect for a 6million caliber production and its style is probably 15 years younger than the caliber. I think it was painted when the Omega caliber was cased in this case. All the 23.7 produced at the same period as this caliber were cased in 30mm average size cases (could vary from 28 to 32mm). Larger cases were found on earlier 'trench' style productions or later as from 1936-37. But the production of the period of your caliber was standardised .
So the dial originally fitting with your caliber was probably 23-24mm, too small to fit in this case, so it was probably replaceed by this one. All this could have been done by a watchmaker before selling it to your family.
Of course all this is deductions from some pictures, the story of this watch could be different, but I'm sure for the case and dial (and probably the hands, the original ones should have been too short for this dial).
You can easily get confirmation of the caliber ref, it is written under the balance.
Whatever its provenance and its modification, it is a family watch with all its sentimental value. I would leave it as it is.

Thanks for sharing all your thoughts and deductions according my watch, now I have idea why I couldn't find anything similiar while researching. And the caseback isn't signed.
It's indeed the only this old watch in family, initially I thought about commissioning to replate case and overall clean up the watch. As someone who's familiar with such watches, you suggest to rather leave it as it is?

Being what it is this watch will never be a collector, its sole interest is its sentimental value as it is a family watch. If you replate it or transform it in any way, it may loose this attraction for you and will not gain any value for collectors. You can have it serviced (in fact if you want to wear it, have it serviced before) and lightly cleaned but that would be all in my opinion.

Thanks for advice, appreciated 😉