The box moves too quickly, i.e., it exceeds any possible setting.
When do you like to have the cubes “static”?
So, the only point when I think it will be possible is when the box starts to move. This will, of course, look not right.
Anyway, delete the animation from the box, and apply that animation on a new Null Object parent while all elements are under that null object.
In the file below, you can use the Layer to switch off the animation. Then cache the solution with a MoGraph Cache. Then switch on the animation again.
Example (Layer animation—on or off)
I have also increased the Dampening of the Rigid Body and set the Box to Moving Mesh.
As a side note, and I assume that is focusing on testing, but just in case someone would argue that this should be doable: The box moves in 2/3 rd of a second 188meter while accelerating and stopping. If we ignore these changes and take the distance-time ratio as average speed [sic], it would be close to 700Mph; that is the simplified version. The actual peak value is much higher. Just to explain that the dynamics system is not built for this, I see no need for it.