If building something so large, you would start drilling down on the shore and then sideways underneath the water as far as necessary. It would be unwise to drill using a rig on the ocean itself. Drilling on the moon is well a moon shot...
It's really hard to explain just how much more difficult that is. This would require digging extraordinarily deep. At that depth temperatures and pressures are absurd. You'd have to be able to keep whatever tunnel you dig from collapsing due to the pressure without causing saltwater incursion.
To be entirely honest I don't think we even have the technology to do this on earth. In space it's feasible but expensive and time consuming but on earth, under the ocean in particular we probably don't even have the technology yet to make that an option regardless of how absurd.
And at that point you might as well just tunnel under solid ground instead. It'd be far easier and at least potentially achievable. But that's exactly why TFA is proposing a lunar collider instead as it'd be cheaper and more feasible than one that is underground on earth.
I’m going to guess it’s still easier than building it on the Moon, where we have notably less drilling capability and the conditions are significantly harsher. Not to mention the cost of equipment transfer.
IIRC more people have spent longer on the the Moon than the bottom of places like the Marianas Trench.
Managing 0-1 atmosphere variation is very different than 1-400. The deep ocean (and deep crust you’d have to go through in spots if you want it to circle the Earth) are extremely hostile to humans.
