How do I install GCC and make on a mac without administrator access or using Xcode?
If you don't have administrator access to your machine, you are still be able to install pre-compiled binary software inside your home directories. Create a folder in your home directory called usr and a directory inside that one called bin, if you want to match the standard directory structure of where make and gcc usually reside.

you can find a gnu make binary for os x here

about make

you can find a download link for a gcc binary for os x here

about gcc

Using these tools successfullly without sudo (admin or root) access is altogether another thing... and you didn't ask about that, and I can't answer that, anyway. It seems like it would be easier to gain admin access through various methods available on the web than to try to build software without admin access. But this, of course, is not part of your question. Best of luck!

(and FYI, I'm pretty sure Brew requires xcode, and if you can get xcode installed, brewnistas enthusiam for Brew notwithstanding, MacPorts is far far more resiliant and mature than Brew)