Frankly this could have used the clunky exposition, because although all of this is loosely stated in the film itself, it's so vague and confusing, that... well, there's a need for a page-long explanation for it.
I think what throws most people is the fact that the sub sets out to find Godzilla on the ocean floor, and then proceeds to find Godzilla on the ocean floor; it's kind of a "well what were you expecting to happen?" moment when you don't get the implication.
Imagine how creepy it would have been for the sub to have gone out to the Bering sea to find the dinosaur...
and for it to not have been there at all. It's already gone because it's already become Godzilla decades prior.