QUIC is a combination of TLS and TCP essentially, implemented over UDP so that there is some chance that middle-boxes will allow it to pass (there's very little chance to actually use a completely new protocol over IP directly and have your packets received by the vast majority of networks).
HTTP over QUIC will probably do a similar number of round-trips compared to HTTP over TCP, but it will do much fewer than HTTP over TLS over TCP. There's no getting away from SYN/SYN-ACK/ACK for a reliable protocol, but QUIC can put certificate negotiation information directly here, instead of the TLSoTCP approach of SYN/SYN-ACK/ACK/ClientHello/ServerHello/ClientKeyExchange/ServerKeyExchange.
Additionally, QUIC supports multiple streams over a single physical connection, and correctly implements packet ordering constraints and retries for them. TCP supports a single stream over a connection: any delayed packet will delay the entire stream. In QUIC, a delayed packet will only delay packets from the same logical stream, packets from other streams can still be received successfully on the same connection.
This feature is heavily used by HTTP/3: HTTP/2 introduced a concept of HTTP streams, but all HTTP streams were run over the same TCP connection, so over a single TCP stream: a slow packet on HTTP/2 stream 1 will delay all packets from HTTP/2 streams 2, 3 etc. With QUIC, an HTTP/3 stream is a QUIC stream, so a single slow request will not blkc other packets from other requests from being received.