Dave,
I think your animation is happening too slowly. Stamping something into metal is an (almost) instant event. So much so that any stressing sounds would be covered up by the sound of the actual hit of the stamp.
On the other hand, if the lettering was being pressed (as in hydraulic/mechanical press) into the metal, it would happen much more slowly. In this case, there’d be no hit (stamp) sound, only the sounds of the metal stressing (stretching/tearing).
Your example seems to be a mixture of the two above situations, which just doesn’t happen in the real world.