A lot of people don't realize that all these so-called issues with TCP, like slow-start, Nagle, window sizes and congestion algorithms, are not there because TCP was badly designed, but rather that these are inherent problems you get when you want to create any reliable stream protocol on top of an unreliable datagram one. The advantage of QUIC is that it can multiplex multiple reliable streams while using only a single congestion window, which is a bit more optimal than having multiple TCP sockets.

One other advantage of QUIC is that you avoid some latency from the three-way handshake that is used in almost any TCP implementation. Although technically you can already send data in the first SYN packet, the three-way handshake is necessary to avoid confusion in some edge cases (like a previous TCP connection using the same source and destination ports).

I have a suspicion that the 30 second loading time is not caused by TCP slow start.

Slow start is about saving small-integer-numbers of RTT times that the algorithm takes to ramp up to line speed. A 5-30 second load time is an order of magnitude off, and almost certainly due to simple asset size.