Sort of. The very first compiled binary of any new language has to first be written in a language that already has a compiler, and the very first compiler of any high-level language at all had to be written in assembler.
Ultimately, if you can't write a Quine directly in logic gates, which you can't because no microprocessor can output another microprocessor, you need something external to the "universe" of the language.
Ultimately, if you can't write a Quine directly in logic gates, which you can't because no microprocessor can output another microprocessor, you need something external to the "universe" of the language.