Well, don't just talk about it, NP --- go write it up!
Along with Godzilla, it would be cool to throw that 1950s Kirby monster comics stuff into the mix. My only concern would be keeping it light enough and not dwelling on stuff like how many thousands of people must get killed every time the monsters rumble through Tokyo or NYC.
If you adopt the idea that this has been going on for decades [dinosaurs discovered in South America by Professor Challenger around the turn of the century, a giant ape climbing the Empire State Building in the 1930s, atomic-powered beasties and alien behemoths from the 1950s onward, dino cloning in the 1990s], then there are surely safety drills in place, and the major cities can be safely evacuated.
But I also like the idea [using the "Island Zero" issue of Planetary as a starting point] of introducing kaiju into an Infinite campaign --- it's just a matter of explaining why there are giant monsters and the world at large hasn't heard about them [which isn't too hard, actually --- have the kaiju attack isolated islands in the South Pacific during the 1950s instead of Tokyo, so we have few survivors + a major coverup].