Welcome tiquy
B.Altman did sell watches, it was a pretty snazzy place, they could have had a private label arrangement with Omega.
Or it could be some watchmaker made a repair using an Omega winding crown he had that fit ?
Is it a manual wind watch or self winding?
Are there any hallmarks on the case to indicate what metal, they are sometimes found where the band attaches.
Might be worth taking to a jeweler to change the band to a leather strap, they can also open the back to see if an Omega movement lies within . . .