IWBNI there were a pause between waking-up the player from sleep and the music actually starting. Most amps take a few tenths of a second between getting the control signal and actually producing output, so that's a few tenths of a second of lost music. It's not a problem on boot-up, of course, as the amp is turned on with the display during the boot process.

Alternatively, it could rewind the MP3 by a second or so; that would avoid missed music without muting Tuner or Aux any more than necessary.