Linux provides netconsole which is an output only equivalent of
dmesg over the network using broadcast udp packets. If configured in the boot command, it starts sending as soon as the interface is up.
Note, for full console input/output, I have used in the past an ipkvm hardware device, as linked to in the comments by roaima, that plugs in to the usb and appears to the BIOS and OS as keyboard and mouse. It also plugs in to the VGA video ouput, and converts the analog signal back into an image which can be sent over the network to appear in your browser as an animated view of the system you can control completely at a distance. Presumably, hdmi versions of these exist too.