Kalam

[LadyForCamus]

But none of those states of affairs could exist without time.

You're right. I certainly don't mean to imply that Aristotle believed in a static universe, or that things don't develop over time. Everything is in motion, which means time.

The point is that Kalam argues for a thing that happened at one time, which then might have stopped.

Maybe I’m just not as well-read on the subject, but where in the Kalam does it argue that the event that started the sequence might have stopped, or could stop once the sequence has been initiated? 

An analogy would be dominoes -- the first domino falls and starts the sequence, but then the first one is out of action. It could lie there, or the cat could eat it, or whatever, and it wouldn't affect the ongoing fall of the dominoes. 

So that's a temporal starting point, as is the Big Bang. (A series per accidens, because the cause of the previous step could disappear, and the chain would continue.)

How does anyone know that the chain would continue if the cause of the Big Bang disappeared, especially considering we don’t even know what the cause of the Big Bang is?

Aristotle believed in an eternal universe, that has always been going. So there was no point when the first domino hadn't fallen yet.

Time is a dimension of even an eternal universe, no?