That really depends on where you are. I live (and play everyday) in an area that is super muddy bottomed, and I had the chance to talk to a contractor who built the piers and such that you'll see at rich folks' homes. He told me that even in the areas where I sink up to my calves in mud, the reason I don't sink any further is the bottom gets pretty firm pretty quickly, around abouts just over a meter or so. I think he said he buried the posts only around two meters deep, starting where the mud bottom is, and those things held up for decades through gnarly storms.

So imagining godzilla's heels as giantish, I would bet they wouldn't sink more than a few meters into the bottom, especially considering they are still probably car sized on the stiletto surface area.