How do you know that the compiler that was used to compile your compiler was not backdoored (or binutils/glibc/bash)?

You may instead want to look at the bootstrapping work done using stage0, m2-planet, GNU Mes, etc.

https://bootstrapping.miraheze.org/wiki/Stage0

https://guix.gnu.org/manual/en/html_node/Reduced-Binary-Seed...

It starts with a hex monitor of less than 500 bytes and bootstraps all the way up to gcc, all from source.