I'm no cryptographer, but I would say that it is indeed the case that you can assume that two parties can derive a shared key over an untrusted channel. The post Cryptography Right Answers PQ [1], linked in another comment, addresses this in the section "Key Exchange". Rather than thinking about Diffie-Hellman directly, you would turn to a Key Exchange Mechanism (KEM).
Before post-quantum cryptography concerns, KEM were indeed mostly built on top of Diffie-Hellman key agreement, but you could also build one on top of RSA, or on top of some lattice constructs. But you wouldn't build one yourself, there are good constructions to choose from! The OP actually has a 3-part series on KEMs, although I don't think it addresses post-quantum issues [2].
Just want to point out that the article specifically says to use an authenticated KEM (AKEM). A normal, unauthenticated KEM would not work as it provides no authentication. There are no post-quantum authenticated KEMs as yet.
There are post quantum KEMs though that authenticate with a classical mechanism, which limits quantum attacks to interactive from the previous total breakage of recorded ciphertext exchanges (e.g. Wireshark capture at a router encountered in both directions of the traffic flow).
Google's post-quantum TLS experiments that were done in public via Android Chrome are such; basically you just do normal TLS handshake but stack the key derivation from the traditional DH-type perfect-forward-secrecy exchange with a post-quantum-perfect-forward-secrecy exchange that you all seal under the same handshake authentication, and where you make sure to only use post quantum symmetric primitives to fuse the traditional session key material with the PQ session key material such that you don't rely on either one's resistance to keep your secrets secret.
Sorry I don't have a link quite on hand right now.
OK, sure. As far as I’m aware, nobody’s actually made that into an actual AKEM proposal though. (I wish they would, as I think many applications would be fine with pre-quantum authentication and post-quantum confidentiality).
One thing to note about authentication in DH-like systems is that you can derive symmetric key without authenticating the parties, establish secure (but unauthenticated) channel with the resulting symmetric key(s) and the do authentication inside that channel in a way that will only succeed if the symmetric key used by both parties is the same (this is called channel binding). For example SSH2 and many Active Directory related protocols do this.
DH + HMAC on its own doesn't give you authentication, anyone can establish a symmetric key. It's possible to build authentication on top but it requires pre-shared data or PKI.
The way DH is used typically for encryption (ECIES) or in TLS doesn’t give you authentication. But you can get authentication from DH alone, without PSK or PKI. See https://neilmadden.blog/2021/04/08/from-kems-to-protocols/ for some details on the security properties of various types of DH.
I meant that some data still needs to be distributed securely, just it's the sender's public key rather than a PSK. I recon "pre-shared data" was not the best choice of words...
