When Linux finishes initializing itself it runs /sbin/init (it is one path it tries among a bunch of others, though i think /sbin/init is the first it attempts to run - you can override that with the init= kernel parameter at boot time, e.g. in GRUB). So just make /sbin/init be your binary and make sure it can run by itself without any other initialization and it should work.
In fact, init=/bin/bash is the traditional way to gain root into a system for which you have forgotten the password. Assuming the filesystem is not encrypted.
