Thanks for the questions. I will try to answer them but feel free to come back to me if needed. :)

The standard model of cosmology includes dark matter and the big bang. Therefore, finding dark matter will allow us to fill one link that is still missing: what is the exact nature of dark matter. So far, we indeed do not have any elementary particle explaining it.

Where do you think we will go from there if the big bang theory is eventually unraveled?

In fact, things happen in the other way round: we usually construct dark matter models in a way they agree with cosmological data.