No scientific Theory can be proved - it can only be disproved. That is in the nature of science: a Theory is simply a Hypothesis that has satisfied many tests and defeated may attempts at disproof. However, a theory can be tested - and frequently is. The theory could very easily be *disproved* - by finding human bones in the same strata as dinosaur bones, for example. Or any other mixture of remains from what are regarded as widely differing times. You can also see evolution in action - for example, in the development of antibiotic resistance in bacteria. The large the species you want to see evolution in, the longer it will take, because it seems to take a few hundred generations for evolution to show up clearly. In bacteria, that may be only months; in mammals that is usually the better part of a century.

So I guess my next question would have to be, what kind of test (or process) would one have to run to figure out what did not happen at the beginning? And if it no such test exists, then should science be exploring that question, or leave it up to religion?

The theory of evolution has been validated more than most theories. It is as close to fact as you can get in a theory. Even though it is modified as more is learned. The scientific method is the best way to evaluate evidence. Scientific advancement would stop if it weren't for the scientific method.