While snow is mentioned in the text, ice is not. But, it’s an interesting cosmological idea even though it has a problem with the empty space idea.
I visualize everything is contained within an immeasurable ice sphere. Whenever new 'space' is needed to contain new matter, the inner surface of the ice sphere melts some more. Ice has more volume than water, so when the ice turns to water, there is a little left over space.
I was kind of surprised to see that picture, as it nearly matches my crude model.