I have one very similar from 1947, my guess is yours will be around the same year, give or take, you will be able to tell once the back is off as there is a number stamped on the caliber which will date it accurately.
It is essentially the same watch Omega produced for the military during the war, 110,000 of them apparently, they then put prettier faces on the post war.
I have a chunkyish Hirsh strap on mine which gives the watch some heft, otherwise they look too dainty as they are small by todays standards.
By the way Austin Kaye on the Strand in London sell them for around a grand, the 38mm versions go for around a grand and a half, so not too shabby.