The first compiler for a language is written using another language, and often the first real test of a new language's usability and power is to bootstrap itself by writing the second compiler in the language itself.
A common question is "how was the first compiler created if there were no other compilers to use?", and the answer is that it was written directly in machine code without the aid of a higher level language.
>can you be more specific, about which language you
>are talking about as the word "language" is broad
Specifics are irrelevant. The question is about programming language design/implementation in general, and being more specific won't change the answer.