They say the a-bomb proved the equation. Maybe, but measuring the mass of the particles after the explosion must be quite a task.
That's only one of the many dramatic pieces of evidence. The important data after the explosion is the energy release. The calculations before the release contain both the mass converted and the equivalent energy release. The theoretical calculations made before the explosion are used to engineer the device and its energy release.
The pion-beam cancer therapy machines also confirm the equation. (And time-dilation, to boot.)