When I launched Overwatch there was no sound. I couldn't hear Winston's speech or any other audio in game. When I was in another game just before that I had audio, when I launched another game I had audio, and on the xbox menus I have audio. All of my sound settings are set to 100 and I even tried resetting them to default. I went into the xbox sound settings and nothing there really effected the sound levels. Did I accidentally do something or is it a glitch with the game?
This seems to be related to the Xbox One's standby mode. Putting the console on standby with Overwatch running often causes this issue.
Force quitting and restarting the game seems to fix the issue. You haven't messed up with any of the settings, don't worry - just a buggy game (I had that issue once on PC too).
Try to restart the game and then the console itself if the issue isn't fixed.