Infinite similarity or absolute homogeneity is logically impossible and thus truly empty space cannot ever exist anywhere at any time in any amount.
Trying to explain "how God works" is what people have been trying to figure out for thousands of years. When someone figures it out, they seldom shout it out, but rather choose to hide it because they don't want others to know. "Information is power" - almost.
If you ask how anything works, you might get an explanation. But then from that explanation, you can ask again how each part of the explanation works. From that, you can ask again, and again.
Eventually you begin to see that you are really asking how everything works even though you only started with one thing, because down at the very bottom of it all, you find principles that apply to everything, not merely the one thing you were asking about.
But still pursuing, you finally come across a principle of how things work that seems to have no explanation. It "just is". That is where most brilliant men stop. How much more do you really need to know?
You can ask why does gravity work. Science, currently won't tell you except to say, "it just does" but that is not to say that there really isn't any explanation. It just means that there is a limit to rational questioning of how and why.
I could answer your question with, "God works by creating distinction", but without showing you the entire road map as to how that action creates all else, how would you believe me or even really understand what I meant.
You might just ask, "But how does God create distinction?" But the answer to that one isn't really a "how", rather more of a "why is there distinction", because distinction doesn't get created so much as redistributed, like energy that cannot be created or destroyed, but rather merely changed in form. So from where did it come?
The mathematical probability of a truly empty volume of space of any size at all, is zero. Empty space cannot ever exist anywhere at any time.
For something to exist only requires that there be distinction between points. In fact, it is distinction that makes them points. But how could any 2 points be infinitely identical? How could all points within a volume of space be infinitely identical? They can’t.
Infinity is an interesting concept. No matter how infinitely close in comparison something might be to something else, there is always still another infinite potential distinction to examine. In effect, no 2 points can ever be infinitely identical in any way because infinity can never be reached by anything in any way.
From this thought, we can deduce that at no time has the universe ever been a nothingness, nor can it ever become a nothingness. The universe could never have begun nor can it ever end.
Distinction and energy both "come from" the same source - logical necessity (i.e. “God”).
Logical necessity is not the same as rational necessity wherein something has a purpose that necessitates something so as to serve the purpose. Logical necessity refers to how/why it is that a big box cannot fit inside a small box. It is a matter of definitions.
Logical necessity is a matter of defining/identifying one thing in regards to another and thus making distinction. In so doing, a man "creates truth". Truth is not reality, but rather a mental model of reality. When the model in the mind matches the reality, it is called “truth”. So you really have the physical reality and the mental truth, both being created by making distinction. In the physical sense, the universe gets created. In the mental sense, a mind gets created.
Distinction - why is it that a thing cannot also be what it isn't?
Because it "just is" - "I am that I am" (or more properly "It is what it is").
If one focuses on even an infinitely small distinction and then creates all else relative to that size, the initial distinction will be significant and thus no longer infinitely small. Size is relative. Is a mountain big or small? Relative to you, it is big, but relative to a galaxy, it is minuscule. You will never really be able to see the atoms of which you are made because relative to you, they are minuscule.
All creation is made from minuscule distinction that can never be absent. It can never be absent because of logical/mathematical necessity, “God”. The universe never began, but merely changes form.