In the late 60s, the Incompatible Timesharing System ran on a PDP-6 without any paging hardware (i.e. an MMU in modern terminology). See the Jargon entry for BLT, for example, which states (my emphasis):
... one resource-intensive memory-shuffling operation done on pre-paged versions of ITS, WAITS, and TOPS-10 was sardonically referred to as "The Big BLT".
The MIT Dynamic Modeling group adopted ITS for their PDP-6 and PDP-10 (named MIT-DMS). Initially, there was no disk to provide swapping store, so they ran a non-paged ITS until around 1973.
There is a copy of ITS for MIT-AI and MIT-ML (but not MIT-DMS) from 1973, but there is no trace of support for running on a PDP-6 or any possibility of running without virtual memory.
I believe the majority of software development in the non-paging era was done using DECtape so, if an pre-historic ITS was to be found, it would probably be on such a tape. Another possibility is paper tape, since this was often used to load software for booting.
Does anyone know where this (a non-paging ITS) could be found?