In the early days (late 60s), the Incompatible Timesharing System ran on a PDP-6 without any paging hardware (i.e. an MMU in modern terminology). (See "The Big BLT".) It was later moved onto a PDP-10, and around 1970 a pager was installed and ITS was modified to use virtual memory.
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.
Would you please check your archives? Thanks a lot!