How can I cold-boot a mac with FileVault enabled without physical access to the mac? If I had a Linux machine, I'd be able to enter the password for the encrypted boot disk in a serial terminal during the boot process, via another machine connected to the serial port I can SSH into.

Is there a way I can do this with macOS as well?

Or is there maybe another setup that allows me to unlock FileVault during boot remotely?
You can reboot the system without requiring password entry using the fdesetup utility:

sudo fdesetup authrestart


See man fdesetup for details.