GCC itself is written in C. Thus, in order to install it, you need a C compiler. This is a catch-22. You're not missing anything. In fact, there is a rather famous Ken Thompson essay, “Reflections on Trusting Trust” reflecting upon a related aspect.
You need to get a C compiler from somewhere. Whoever built your custom distribution surely had one, as you can't build a Linux kernel without it either. They ought to make it available somewhere.
Other than that, you'll have to cross-compile gcc (and binutils, and C library headers, etc.) from a distro where you can install a compiler. This is how someone builds the a distro for a new platform. It's also possible that if your platform is embedded, no one expects you to run gcc on the device itself, and instead they expect you to cross-compile any software you need for the device. In that case, your embedded distro should provide the cross-compiler to use.
Best Answer
What you actually want to do is
clone
the repository. Here is an example: