I understand bootstrapping, but at some point there has to exist some outside compiler in another language or a hand-compiled version of this otherwise the chicken and egg chain never ends.
The very first compilers were tediously written in assembly. Bill Gates wrote his first version of Basic in assembly. I believe all early Fortran compilers were written in direct machine code through punch cards! Coding in assembly is not all that bad :). Once you got some compiler going, you can write more complex compiler with it and keep adding more syntactic sugar :).
Coding in Assembly was a gas! I wrote applications in IBM BAL in the 70's. G/L, Payroll, Inventory. We did it in part because we had so little memory (typically 64K to 131K), we had to squeeze every drop we could out of available memory.
I worked on Univac 9400s. We received the O/S in source code form (Assembly) on tape. We ran it through a parametizer (PROC), compiled the resulting source, and that's what the customer ran with.
You haven't lived until you've stepped through your code one instruction at a time, displaying op codes and raw binary data on the maintenance panel lights.
You can use any language available in the machine to create the first, most basic compiler. You can also use a cross-compiler if a compiler for the language already exists for another machine. If all else fails, you can write the proto-compiler in assembly.