Hi. Please, take a second to consider my proposal as follows: if your Step Functions is ready to go with the Lambda in it, what you need is just configuration of the API Gateway:
1. You´ll need to create an API and resource
2. You´ll need to create and configure a method (GET, POST, etc.)
3. You´ll need to create an IAM role associated to that method for execution of the Step Function
So, I´ll be more than happy to help you with this one. I´ve been using API Gateway and Serverless (Lambdas, Step Functions, Workers, etc...) in my company for more than 6 months now and have also helped other freelancer´s employers with Lambdas and Gateway APIs.
Looking forward to knowing the details. Thanks.
Fernando