A generator without permanent magnets can be used as a amplifier. The extra power comes from the power provided by mechanically rotating the shaft. The magnitude of the output signal is then proportional to the shaft rotation speed and the field winding current. Since extra power is being added to the system via the shaft, you can get more power out than you put into the field windings. If you keep the shaft rotating at a fixed speed, the generator can be thought of as a amplifier from the field current to the output.
One problem with this is that these generators usually put out AC. That can be rectified, but will still have some ripple. If you wind the generator with enough poles and spin it fast enough, the AC output frequency can be higher than your highest frequency of interest. In that case, it can be AM demodulated to yield the final amplified signal.
Rigging up something like this to work at audio frequencies will be tricky. However, you can demonstrate the concept without too much trouble at lower frequencies. Connect a LEB (light emitting bulb) to the output of the generator and spin it to get typical line frequency out, like 60 Hz. Now you can control the lightbulb, or a bank of lightbulbs, with much less power than it takes to drive them directly.
The alternator in your car actually works on this principle to keep the rectified output of the alternator at the right voltage. The alternator spins at whatever speed it spins at. The control system modulates the field current so that the alternator output produces the right voltage to keep the battery charged but to not overcharge it. In this case the "amplifier" is being used as a voltage regulator, but the overall concept is the same. Less power is required to run the alternator field windings, which comes from the 12 V DC, than the alternator puts back onto the 12 V DC line. The extra power comes from adding a mechanical load on the engine.