By "induction," I'm not referring to the scientific evidence, although much can be said about that. Rather, are there inductive philosophical grounds for affirming the KCA's key second premise?
1. Whatever begins to exist has a cause. (Premise)
2. The universe began to exist. (Premise)
3. Therefore, the universe has a cause. (From 1 and 2)
I suppose that (1) can be supported through induction in addition to the ex nihilo principle. Our experience of things that begin to exist leads us to believe that they are caused. As far as (2) is concerned, one could point to the other known aspects of the universe. Are the universe's limitations the result of finite characteristics or infinite ones? The universe's finitude is almost built into the very concept of its having limitations.
With this in mind, what is the probability given the background information and our knowledge of the universe's other qualities that the universe's past is infinite? It would appear to be very low, unless of course we have compelling evidence to believe that it's infinite. But, there just aren't any arguments for the universe's having an infinite past. Skeptics spend almost all of their time trying to answer arguments for the universe's finite past.