Docker Builds
As has been stated many times, Serverless and Lambda are not the same thing. Lambda is 100% a serverless service but there are other ways to run compute in a serverless architecture. Two other AWS serverless compute frameworks called Elastic Container Service (ECS) and AppRunner offer managed container environments where you bring a Docker image and AWS will place and manage the operation of that code.
Building containers for Rust is not much different than with other languages but this site would not be complete without addressing some of the different options.
📄️ Alpine Image
Building a Rust project to be deployed on an Alpine image