The USB on the mixer is for Firmware updates, and can also charge a connected device like a phone or ipad. Would need to know more about your pc to know what is possible. If your pc has either an expresscard slot, or thunderbolt port, there are cards and/or adapters to use with firewire.
Another option would be to purchase a dante card for the mixer, and connect via ethernet. There is an avb card in the RM mixers, but audio over avb is not done cooking yet. You can always wait for that implementation, which would also be an ethernet connection. No eta at this point for AVB audio implementation.