Yes. This is a very advanced endeavor. For those with a board that stopped working who might read this in the future: I wouldn't necessarily recommend trying it solely in hopes of fixing your board, since you will spend a lot of time on it and it is likely the ATSAMD11 firmware is not the cause of the problem.
I do think it is a very interesting project for someone who wants to learn more about the subject or install a custom firmware on their Nano Every.
The SWD header of the ATSAMD11 is broken out to some small test pads on the bottom of the board. The pinout is documented in the "Full Pinout" PDF that is available for download from the Nano Every's documentation page:
https://docs.arduino.cc/hardware/nano-every#resources
You will need an SWD programmer for this. It is not possible to use an ISP programmer like we do for the AVR architecture boards.
There are instructions here for compiling the firmware from the sketch source, but that is only necessary if you want to make modifications to the firmware. The official firmware binary is available for download here:
For those who are interested in building from source, note that those discussions are somewhat outdated because the problem people ran into with the compiled sketch size exceeding the available memory (arduino/ArduinoCore-megaavr#103) was resolved since then.
