The next state is not uniquely determined by the prior state, so asking what makes the ball roll shows that you don't understand the claim (non-determinism ) at hand.
If you were able to perfectly balance the ball on a perfectly constructed dome, blah blah, would the ball stay static indefinitely or would it start rolling down some arbitrary path?
This is completely contrary to our intuition about Newtonian mechanics. The question "given this situation, what would happen?" typically has a unique answer is typical. If it does, we have determinism. The observation of Norton's dome is that mathematically this question does not have a unique answer in all situations.
Not a different question, not an essay, not hand-waving, just focus on that very concrete question.
Are you asking about a fictional universe governed by the Newton equations and nothing else? Then I can not answer your question because the question builds on a faulty assumption: That this universe is deterministic and that what is determines what will be. Mathematics shows that to not be the case.
The only possible answer to your question in the second case is: It can not be known or predicted what the ball will do.