For any practical purposes, it is best to simply use the full complex software stack on another computer to generate binary code meant for that new architecture.
If we'd really need to bootstrap a compiler from scratch, then a possibility would be to hand-code a Forth system, and then find/modify/make an assembler written in forth; then write a compiler for some small language (scheme?) in that assembler, and then from scheme you can easily get to some C compiler that can compile the full GCC.
If we'd really need to bootstrap a compiler from scratch, then a possibility would be to hand-code a Forth system, and then find/modify/make an assembler written in forth; then write a compiler for some small language (scheme?) in that assembler, and then from scheme you can easily get to some C compiler that can compile the full GCC.