How fast can a generator convert water into hydroelectric energy?

Hydroelectric generators do not convert water into anything. And even assuming that the question means to ask: how fast does a hydroelectric generator produce energy? the short answer to that question would be instantaneously.

A hydroelectric generator produces electricity by converting the kinetic energy of moving water into electrical energy via alternating magnets which are spun by the turbine getting hit by the moving water.

If the question is: How much energy is produced by a hydroelectric generator, then that answer depends on the size and efficiency of the system.