For digital signals, 0 dB usually means full power. That scale is typically denoted dB FS ("full scale"). Other scales are dB SPL ( "sound pressure level"), which is what you where probably referring to.

So in other words, you are probably saying that reducing the signal loudness is reducing your signal-to-noise ratio and thus your audible dynamic range. However, your noise floor is probably far higher than 0 dB, more like 20-30 dB SPL (if you're lucky!). A normally-loud (that is, non-damaging) music playback will probably be at about 50-80 dB, so your usable dynamic range will be about 30-60 dB, which translates to about ten bits. Most environments will be worse.

0 dB are actually pretty hard to come by. Even well-insulated acoustical measurement chambers only go to about 10 dB. Only several meter of acoustic foam and a solid foundation and a purpose built air conditioning can go down to 0 dB. So, umm, 0 dB is usually a rather useless figure for non-scientific purposes.

That 24-bit DAC does nothing for you after the sound turns analog between the DAC and the speakers/amplifier. That's why I said the second step may not lose you bit depth if your DAC is floating point or as you say 24bit, but on the third step you will lose something.