I'm reluctant to declare myself 100% sure but I think your one is genuine. I have an Omega Geneve in stainless steel from 1971 with a 21 jewel 1481 movement, which has steps like that. I think I can see 1480 written on yours which would have been the 17 jewel version at the time. As a quick test if you push in the crown and then release it fully the date should move forward one day. NB Only do this between 3.00am and 9.00pm to avoid damaging the date disc.
The pictures below show my watch that is 100% authentic and original.
The pictures below show my watch that is 100% authentic and original.


