I haven't worked on collision detection since the 1990s. But convex hull collisions are very fast with GJK. And the space swept by translating a convex hull is

I haven't worked on collision detection since the 1990s. But convex hull collisions are very fast with GJK. And the space swept by translating a convex hull is itself a convex hull. So continuous collision detection (no fly-through) is possible that way. But that's usually overkill. Objects that move more than their own dimension in one frame time are usually bullets, and those should get special handling.