If you want to perform Git operations inside an AWS Lambda written in Python, you can decide to use the GitPython library. However, it needs git to be installed on your system.
In order to package git, I discovered a really nice tool: lambci/yumda. It's a docker container that overrides the yum installer to deploy the library you install, including all its dependencies, into a separate folder called /lambda/opt. So all you need to do is to yum your git, and zip the content of the folder.
Here is an example of a script that packages both GitPython and git into a zip file compatible with AWS Layers:
Then you can send this zip to an S3 bucket and create your layer easily. The nice thing about running this script inside a CodeBuild is that all tools, such as docker and pip, are already installed. However, for docker, do not forget to enable the Privileged Mode.