QUIC offers both 0-RTT and 1-RTT connection setups, meaning that at best QUIC needs no extra round-trips at all when setting up a new connection. The faster of those two, the 0-RTT handshake, only works if there has been a previous connection established to a host and a secret from that connection has been cached.
QUIC allows a client to include data already in the 0-RTT handshake. This feature allows a client to deliver data to the peer as fast as it possibly can, and that then of course allows the server to respond and send data back even sooner.