First of all - congratulations on your new watch.
The case is indeed sharp.
The original crown for a 168.004 is almost entirely hidden.
IIRC Crowns were replaced as standard in a service.
The original crowns are no longer available.
There are two types of replacement crown ( shared with the 168.010)
1. The knurled cylindrical shape.
2. The knurled domed shape.
Both stick out from the mid case.
You appear to have the second type.
It is possible a previous owner had it replaced at service because the originals are damned near impossible to use.
Pic of original for reference
p.s.
If you were referring to hidden crown Constellations as ‘jumbo’ this is a misleading term used by nefarious dealers.
They are very slightly larger diameter than a dogleg or lyre lug but the term ‘jumbo’ is reserved for the significantly larger Constellations predominantly sold into Japan and the far east.