Omega 168.0010 legit?

Looks legit. Sharp case. Movement photo?

I think the ref number indicates service case see what the experts say.
Nonetheless it looks good. Was it described as original or service case?

How about a shot of the inside of the case back?

Omega Vintage site

These originally have a recessed crown, so this one looks like a service replacement. Given the overall pristine look of case dial and hands I suspect this has been back to Bienne for a service with major Omega service.
Which would give you a very nice functioning watch, only many vintage parts replaced. That’s what they do. Can you find out if that is what happened?

Welcome @HanYolo2

This is a bit of a conundrum.

If it has the extra 0 then it will be at least a service back.
Given the excellent condition of the case, I would suggest a full service case.
This may explain some of the anomalies in the caseback and case

The dial and hands are correct for a later 168.010. (onyx with lume and pencil hands)

However, the observatory should be the brickwork variant and the stars less well pronounced.
(the service back might explain this)
But, the mid case should have a definite cut out for recessed crown.
The mid case above looks more like a 168.018 case, - it may be that Omega only produced a service case in one style.

whatever the explanation, it is a very handsome watch, but it is certainly not as it came out of the factory in 1967 - whether that bothers you might depend on price paid and what you were looking for in a watch.

here is what the two variants of 168.010 case back look like.
the gold cap version has the replacement crown, the SS has the original crown (apologies for the less than sharp image)

the OVDB info can be misleading.
Omega added the extra 0 into their search function (for some unknown reason)
the original reference is 168.010
it was never produced in 1962 - this was the earlier 168.004.
the first 168.010s appeared around 1966 and did indeed carry a cal 561movt but these variants are quite uncommon

Thanks. I was a bit confused when I found the extra zero there.