The ball bearings are behaving as a solid because the forces between the steel balls (i.e. friction) are large enough to hold the balls in position relative to each other.
If you apply enough force to a solid you will cause it to fracture or to cause plastic flow. So for example if you attached a string to the ball and pulled upwards with enough force it would cause the steel balls to flow over each other and the table tennis ball would move up. The force required is related to the yield stress of the solid fromed by the steel balls.
You can make the steel balls behave as a fluid by making a gas flow through them. This creates a fluidised bed. The gas pushes the steel balls apart so the friction between them is removed, and in this state the steel balls will behave like a fluid and the table tennis ball would float upwards.
Alternatively just shake the beaker. This is equivalent to adding thermal energy i.e. heating the system until it melts. If you shake the beaker you'll find the table tennis ball floats upwards.