how godzilla and the mutos survived

The survival of these creatures could be due to almost any number of things. Honeslty though, since I'm not a scientist, I am having a hard time wrapping my head around the most logical reasons. Suspended animation is one idea, but it alone cannot carry the day. There has to be something more to it, but what could those reasons be that they'd escape our advances in technology so thoroughly as to remain hidden until now?

I'll be waiting for the explanation in the movie, but right now, I'm stumped.

Going off of what Somthing Real said, I would have to agree that they may mature at a slow rate, however, I believe that the MUTOs in this movie are relativly young.

These are the newest generation of MUTO, which were found, captured and experimented on. Alone remains a hateful, bloody instinct that Godzilla alone is their greatest enemy. Their rival species.

Well, given that the larger an animal is, the longer it will live overall, I'd say that being this large simply entails extreme longevity, coupled with the fact that the need for conventional nourishment/air intake has all but been eliminated by a nuclear reactor organ system that effectively infinitely powers the creature, as well as their extreme mutative evolution likely extending their telomere analogues to nigh-unending chains, and the ability to hibernate no matter how bad conditions may be, millions of years is just a few months to these sorts of creatures.