How do I get make, gcc, clang, Xcode? It has been almost a week as Apple has disabled downloads from https://developer.apple.com/downloads/ due to a security breach.

If you don't have App Store set up for whichever reason, how are you supposed to be using your brand new Mac for development?

Is there a copy of Xcode hidden somewhere within a brand new mid-2013 MacBook Air?

How do I get Xcode if I don't have an App Store account?  Nothing works without Xcode, I can't even use MacPorts to install the stuff I need, because it all depends on Xcode.
Use the OS X GCC Installer. Download it here, since you have a brand new Mac you'll want GCC-10.7-v2.pkg. This will get you GCC, LLVM, clang, the Developer CLI tools, and the DevSDK headers.