Packaging and Shipping GCC Compiler with all dependencies to AWS Lambda

I want to take the GCC Compiler that is on my machine and all its dependencies and zip them up in a deployment package that I can send off to AWS Lambda (That way I can use a Lambda to compile C code). However simply zipping the gcc executable does not work because it uses shared libraries. Is there an easy way to package the whole thing in one go so I can deploy and use it from AWS Lambda.