How can time and space exist without Existence?
I don't know.
That's a good start. The logical priority of existence is a straightforward proposition: in order for anything to be said to exist
, there must be a state of "existence", just as there must be a state of "heat" in order for anything to be said to be warm (or, indeed, cold), or a liquid state in order for anything to be said to be wet, etc.
It's also not immediately obvious why it's a good idea to suppose that "nothingness" (there being nothing; nonexistence) is some kind of default state of reality, not least because it raises a pretty epic question of how, from nonexistence, there came to be anything at all.