Migrating to Serverless Development from Express

I have been using express with docker for my REST API and now I want to replace it with AWS Lambda and Serverless. When it comes to development, I looked at: aws-sdk-mock for unit testing with mocha and serverless invoke local for calling lambda functions. Before I deploy my Lambda functions to the cloud, however, I was wondering if it’s possible to run them in a docker container (in localhost) and make api calls from my front-end to that container? I saw the serverless-offline plugin which seemed like the solution I’m looking for but reading the documentation I still need to use serverless invoke to call the functions? (I can’t just point my front-end api calls to the localhost).

I’m brand new to Serverless so I was wondering if more experienced users have solutions to this problem or have found better ways to develop and test their code before deploying it to the cloud?