Are you asking about the real world? Then the answer is that you can not perfectly craft the dome and what happens depends on the imperfections.

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.

It is a concrete question! Here's a potential energy function describing a "hill". Here's an object on the hill at this location. How will it move? The question is well formed and complete. And it has more than one answer!