Kalam

[Belacqua]

 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? 

As far as I know, Kalam only claims that 1) the universe has a beginning, and 2) the beginning was caused. 

Beyond that I don't think it makes any claims as for whether the cause needs to continue or not. They'd need additional arguments for that. 

If William Lane Craig and those guys have proposed those additional arguments, I've never heard of them. (I'm not a big fan of Craig.)

Again, though, this is sufficient to separate it from Aquinas, who makes no arguments for temporal beginnings. 

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?

There may be all kinds of arguments as to why the cause of the temporal beginning would have to hang around. I have never heard of one.

But such an argument would have to be in addition to the Kalam argument, which only makes the two claims. Given merely those two claims, it is entirely compatible with a Deist clock-making God. 

Whereas in Thomas' argument, the ongoing necessity of the creator is fundamental to his claims. 

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

I think so! Aristotle thought there was no point at which time began. It's just always been running along. Aquinas thought that this was all that could be proved through logic (Natural Theology) and if we believe in a beginning point then we only believe it through unproven revelation.