Here are two strategies. First, you can go "outside" what you've built, simulating a user's interaction and examining the resulting DOM. In general this is a tool-centric approach.

Another approach is to partition your code into what Gary Bernhardt calls an "imperative shell" of code that touches the outside world and a "functional core" that does not. Then unit test the functional core, which shouldn't require special testing libraries, and validate that the imperative shell works by the occasional manual or "outside" test.