If the floor is truly frictionless, then ANY force, no matter how small, applied for
ANY time, no matter how short, will set the block in motion. The force can then
be taken away, because on a frictionless surface, NO force is required in order
to keep the block moving.
The work done is equal to the kinetic energy you want the block to have. That
can be as much or as little as you feel like giving it.