See if signal is amplified without an oscilloscope
With a DMM, you should first measure the quiescent DC voltages of your circuit and make sure those are correct.

You might be able to read the amplitude of AC signals in the millivolt range with your DMM but that depends on your DMM.


  The problem is, I do not have an oscilloscope and thus no way to know
  if the circuit works.


It's not true that you have no way to know if the circuit works.  You're just not thinking clearly.

For example, you could connect the (AC coupled) output of your preamp to the input of an audio amplifier or the audio / mic input of a sound card on your PC.

Indeed, a sound card can be used, to some extent, as an audio o'scope.

In my previous life as a technician, I sometimes used a signal tracer to quickly determine if a signal was present or not while troubleshooting a circuit.

Here's a video of someone turning a powered computer speaker into a signal tracer.