You must not touch it yourself. You need to find a good independent watchmaker— not a jeweler- to open it up, take pictures of the engravings inside the caseback and on the movement.
That’ll be the info you need.
There may not be a model name in that era.
You could send that info to Omega through their website in order to purchase an extract of archive which will tell you the exact date the watch was sold, and into what country.
If you say where you are located perhaps people can recommend someone.