Big Questions Need Big Tests
The surest way to know if an application is going to work is to actually run it. Big tests boot the entire application before every testcase.
Does your appication run in a browser? Then if a test is going to measure whether it works or not, it also needs to run in a real browser that a real user might use, and it should dispatch real UI events against a real DOM.
Testing big is hard because there can be hundreds if not thousands of things happening concurrently inside your application; including user interactions.