When the James Webb search begins it will be looking at a 3 full moon wide patch of sky and measure dark matter gravity in thousands of galaxies. We think we have seen a couple distant galaxies that have no dark matter. We don't know what that means but dark matter may have evolved just as luminous matter has evolved and changed. We can't look back to a young 2 billion year old universe since gas blocked light until it reionized and became transparent but we will see as far back in time as possible. Later planetary searches will be done.
Finding the unexpected or 'unsearched for' is also a possibility.