There isn't a way to adjust the volume, unfortunately.
However, using Windows 10 Mobile, you can choose a song from your collection in order to use as your alarm.
Here's what I did, and my wife LOVES it. I used an audio editing program on my PC, picked out a nice ballad song, and edited the song to have a nice, gradual fade-in. I also adjusted the dB volume within the song so that the loudest volume was reasonable. I also made sure it took 30 seconds on the gradual fade-in in order to reach that maximum volume. It wakes us up gently so we're both in a better mood.
It took a bit of experimenting to get that maximum volume just right, but it was a great solution for us.