... what next can you optimize? You can put the key exchange even further up front, which may speed up the QUIC handshake.
And that only leaves us with DNS as anything that comes earlier. In addition to IP addresses and transport choices, now folk wish to put keys into DNS as well.
Which may be fine with small Edwards keys. But several KiB of post quantum cryptography key won't fit into a DNS message, which is in practice bound by the size of a UDP datagram.
So what then - we can't do DNS...