Agreed. The photo is somewhat deceptive as well with the crown hidden under the sweaterIt's hard to tell much from a single picture. Needs pics of the crown, caseback (inside and out), both sides of the bracelet and clasp, and the movement to tell much.
That said - this model mostly had a recessed/"hidden" crown - not sure if every version did. If you search the web for omega 166.003 you can see lots of pics, mostly with recessed crowns.
The date window magnifier looks like an add-on. I believe Omega put magnifiers on a few models, but again, most versions of this one on the web don't have them.
The end link fit is not very good. If this is a real Omega BOR, it's likely for a different watch; at least the end links are wrong.