gatorcpa
··ΩF InvestiGatorAfter WWI, American watch companies made numerous examples of ordnance watches and I do not believe the US ARMY stamp on the back of that Omega to be genuine, mostly because it's hand stamped. They had machines for this purpose.
https://www.omegawatches.com/en-us/watch-omega-other-us-army-ck-2179
There were other watches made with the same dial and movement with a Ref. 2384 case. The engraving on these looks more machine made than the Ref. 2179.
Hopes this helps,
gatorcpa