QUIC is a transfer protocol implemented on top of UDP. If you watch your network traffic casually, you will see QUIC appear as UDP packets.
Based on UDP it also then uses UDP port numbers to identify specific network services on a given IP address.
All known QUIC implementations are currently in user-space, which allows for more rapid evolution than kernel-space implementations typically allow.
There are enterprises and other network setups that block UDP traffic on other ports than 53 (used for DNS). Others throttle such data in ways that makes QUIC perform worse than TCP based protocols. There is no end to what some operators may do.
For the foreseeable future, all use of QUIC-based transports will probably have to be able to gracefully fall-back to another (TCP-based) alternative. Google engineers have previously mentioned measured failure rates in the low single-digit percentages.
Chances are that if QUIC proves to be a valuable addition to the Internet world, people will want to use it and they will want it to function in their networks and then companies may start to reconsider their obstacles. During the years the development of QUIC has progressed, the success rate for establishing and using QUIC connections across the Internet has increased.