At this point, you're just trying to ridicule me over my choice of words and not actually trying to interpret them in the context that you yourself set:
they have a sack of muscles somewhere inside their body
Why mention "inside their body" if you didn't mean "deep" inside? All organs are "inside" the body. Therefore, I interpreted your words meaning truly "internal" organs, that that don't manifest themselves on visual inspection, like heart or bladder. Lungs, while technically inside, are peripheral and visibly expand - a critical distinction in this context.
So you specify "inside" and then mock my adherence to that framing, instead of addressing the core biomechanical issues being discussed.
First, let's address the expansion of lungs, because you say "little air", but in terms of volume, lungs are very big. On average, the volume of a human body is about 65 liters. When person fully exhales, the lung capacity is at about 1-1.5L; when expanded, it's about 5-6L. Interpreted charitably, that's roughly 8% percent of the entire human body volume. So realistically, expansion of the body by 8% is the difference between slowly sinking, and floating with the top of your skull (or roughly 1% of your body volume) peaking out of water.
Now, Godzilla, on the other hand, has like 80% of his body above water. Can you imagine, the amount of expansion that needs to happen for that much buoyancy? That's pufferfish territory.
So no, a "tiny percentage" increase in body volume driven by empty chamber "inside" his body would not be enough.