Something like Lemmy could form a pretty good foundation. Onion routing already has created a "parallel internet" that depends 0% on DNS, and Lemmy instances would federate today (with whitelisted federation) via /etc/hosts with no DNS involved. It wouldn't work well, it would have problems, but if someone actually tried to make it work moderately well, the whole model of "admins running servers which it's your problem to get connected to, and then they know how to federate to each other because all the admins talk with each other" could work itself around over time into something that actually had some pretty strong robustness to it.

There are other attempts (Holepunch, Freenet, all that jazz), but actually Tor and Fedi things probably have the best claims to being able to turn into something realistic that didn't need DNS, over time. You just couldn't talk to it until you set your machine up to be able to get the initial connection going, but that's not fatal, the whole internet used to be a lot like that way back when.