Does this game not support it? There was sound in the title menu -> introduction scene -> character creation menu. But as soon as i click on my character to load it, the sound dies off from then on. The first time i tried this, the opening cutscene (without sound ofc) took pretty long to load too.
My headphones are sony MDR-1000X, running the game on windows 10 home edition, if that helps.
Would like to note that its been like this since the beta, i thought it would have been fixed by now.
I have a Logitech G993 and I fiddled around withe a couple different things from recommendations on the web. These two things fixed the issue. Right-click the sound icon in the taskbar, Select Open sound settings, Choose Sound control panel on the right, right click on your headset and click properties, click advanced and turn off "allow applications to take exclusive control of this device" amd switch your default format to "16bit, 44100 hz (CD Quality)". Make sure you restart destiny every time you make a change. If this doesnt work try doing one instead of the other but this is the only thing that made it work again.