As far as I remember, that's exactly how it happens:Humanity's use of nuclear weapons in Japan awaken Godzilla, and humanity's attempts to kill Godzilla with nukes then awaken the MUTOs.
That's what I recall as well. The implications are actually quite disturbing, if I understand it correctly . . .
Godzilla, the Mutos, and whatever that enormous fossil was, are natural aberrations, as opposed to mutants created by man's hands. Truly made Godzilla and the Muto's feel like something primordial. Fuck, the whole Toho roster could be lying dormant underneath the earth, just waiting for the next nuclear disaster. I'm curious what sources of radiation Godzilla was feeding on. I was surprised to see the Muto's doing what Godzilla was doing in 1985, attacking subs and nuclear plants, as opposed to you know . . . Godzilla lol.
You also know what this movie reminded me of? Primal Rage, despite Godzilla and the Muto's being very animal-like in their behavior, they still felt like something beyond flesh and bone. Something elemental.