boot – Create an El Capitan rescue USB using a Modern M1 Mac

I am trying to rescue my dad’s 2008 iMac. It is running Snow Leopard but the most recent OS it supports is El Capitan. It won’t boot past a spinning progress bar on a grey screen, and will not boot into Recovery Mode or Safe Mode.

It seems to me next step is to try a bootable USB stick. I am running into walls trying to make the stick from my own computer, which is an M1 MacBook Air running Big Sur.

An El Capitan .DMG is downloadable directly from the Apple Support page, which provides instructions on how to make a bootable volume, with a major caveat On a Mac that is compatible with El Capitan, open the disk image and run the installer within, named InstallMacOSX.pkg

I used a utility to extract the Install OS X El Capitan.app file from the .dmg and then ran the terminal command from that support page:

sudo /Applications/Install OS X El Capitan.app/Contents/Resources/createinstallmedia --volume /Volumes/MyUSBVolume --applicationpath /Applications/Install OS X El Capitan.app

But this yields /Applications/Install OS X El Capitan.app does not appear to be a valid OS installer application.
When I google this error some results indicate it is due to an expired file, but changing my system date to 2016 does not fix it. I assume the real problem is a system incompatibility.

Surely there is just an ISO I can get and write without all these hoops?s