If your target is a USB audio device - like a USB headset or USB speakers (NOT an MP3 player with USB interface) then you could connect it to something which can act as a USB host with USB audio device drivers. That means not an Arduino, but something much more powerful like a Raspberry Pi or BeagleBone Black for instance.
If your target is basically an MP3 player that allows you to connect a USB stick with songs on it then you're completely out of luck. There's this small thing called time that gets in your way. You can't stream data to something that expects the data to already be there. You can't seek in a file that doesn't exist until the moment you try to read from it. Also you have to act as if you were a USB memory stick, and that's not easy, and certainly not something an Arduino can do. Even things like the Pi would have a lot of difficulty in managing that since they are hosts, not devices, as far as USB is concerned.
The key word here is stream. Your target as to be able to receive a stream of data rather than request blocks of data from a file. USB audio devices can do that, but USB audio hosts cannot.