It's unclear what you're asking for here? The Raspberry Pi Pico and Raspberry Pi Zero are existing and very well documented ARM based single board computers.
Fair enough. I suppose what I'm asking is whether it's possible to purchase a more modern CPU independently of a SOC and design my own single board computer built around that. Can you buy a naked Cortex M0 in a PDIP package? Are there data sheets for it?
A search of the interned didn't turn up what I was looking for, but I'm very new at hardware work. Perhaps newer chips have such tight timing requirements that you can't work with them without using a SOC?
Nearly everything is going to be a SOC because that's what commercial applications need to minimize part count and cost; there's negligible demand for a standalone processor.
If you're just looking to breadboard up a computer but don't want to go back to 8-bit processors, the Motorola MC68000 / MC68008 used in the original Apple Macintosh is a 32-bit processor in a DIP package running at a manageably low frequency and can be found on eBay inexpensively.
A search of the interned didn't turn up what I was looking for, but I'm very new at hardware work. Perhaps newer chips have such tight timing requirements that you can't work with them without using a SOC?