Has anyone managed to get this game running at least 30fps on a low spec rig? Or is there a demo floating around?

Hi ataraxium.

Frostpunk is programmed in such a way that it will benefit more from a robust CPU than a GPU. Once your GPU reaches its utilization threshold by the application, any performance that will make the difference is dependent on your CPU. No demo is available, other than posted YouTube videos of players benchmarking their own PCs. Frankly, the GPU requirements are bloated, while the CPU requirements are way underestimated.
https://gpu.userbenchmark.com/Compare/AMD-RX-580-vs-AMD-RX-480/3923vs3634
My GPU in an "AMD RX 480" and my CPU an "AMD Ryzen 5 2600". I recently upgraded the CPU, which was a slightly worn out but capable and trusty "AMD FX-8320".
https://cpu.userbenchmark.com/Compare/AMD-Ryzen-5-2600-vs-AMD-FX-8320/3955vs1983
Below are my observations, of the same scenario, on a 1366x768 resolution;
Playing the scenario of Winterhome, in a city of aprox. 850 population, in the last day of the great storm, completely zoomed out of the city crater.
"AMD FX-8320" performance, with every setting maxed out and antialiasing enabled -> 15-20 fps flactuation.
"AMD FX-8320" performance, with every setting on low and antialiasing disabled -> 20-25 fps flactuation.
"AMD Ryzen 5 2600" performance, with every setting maxed out and antialiasing enabled -> 30-35 fps flactuation.
"AMD Ryzen 5 2600" performance, with every setting on low and antialiasing disabled -> 35-40 fps flactuation.
As you have noticed, both setups are not exactly low-end, by no stretch of the imagination, but I hope it helps you understand what to anticipate from your hardware configuration. If your PC is indeed low end, then it will have serious trouble coping with this game, even on low.
Taking a look at this thread might help you clear some things up about hardware performance in this game.
https://www.gog.com/forum/frostpunk/really_bad_performance_with_this_game

Thank you for taking the time to lay that out, that's very useful information. It looks like I might have the same CPU bottleneck you were experiencing, so an upgrade may be in order.