This icon is not only 330 feet tall, but it weighs 60,000 tons... not pounds, tons! I'd assume that he's strong enough to lift his own weight, seeing as it doesn't inhibit his movements. But how much stronger is he? 70,000 tons? 120,000 tons?
The only things that are able to harm Godzilla are other monsters roughly his own size.
The army's weapons, no matter how extraodinary, have posed almost no threat to him.