I'm thinking the MUTOS are some alien entity that will threaten all of Earth somehow.
Humanity either awakens it, or inadvertently makes it more powerful in their attempts to stop it, until they finally decide to just let Godzilla take care of it (instead of opposing him as well), despite him being an indiscriminate force of nature.
I dunno, the gist of the trailer is that the military's primary concern is actually the MUTOs. Something about them puts them on a higher priority/threat level than Godzilla himself. Besides, the lore of the atomic bomb testing is apparently that they were attempts to kill Godzilla that failed. So at this point the cover up may just so that humanity treads as softly as possible around the big G because they already know he's unstoppable.
But now they need a 'god' to intervene because they have no other option.