Go to your music player in your dashboard before you boot up your Xbox 1 game (I.E. Halo 2)
Choose where to play your music, may it be your MP3 player, computer network on the Xbox 360 itself.
Start playing your music, get it at a moderate volume and make note of what level you leave it at (You won't be able to change this once you're in your Xbox 1 game unless you exit it.)
Put in your Xbox 360 game, hit B to back out of the menu and then the game will start.
Your game boots up, but your custom soundtrack doesn't turn off! Sweet!