For the AWS marketplace integration, we have checked the sample code of Serverless integration for SaaS products. The samples provided, it is based on AWS Lambda functions for registering new subscribers, subscribing to SQS etc.
Can we implement all these functionalities with our database, functions etc, instead of using AWS lambda and dynamo DB?
Also in the examples, some lambda functions are there like stream handler, entitlement-SQS, subscription-SQS-handler, grant-revoke-access-to-product etc. How can we trigger if we use our APIS?
Yes, the AWS Marketplace SaaS integration documentation states:
All you need is an endpoint that can receive that POST in order to integrate. If you want to trigger any additional AWS API calls, your endpoint could make use of an AWS SDK. There are also requirements surrounding what your POST endpoint must do in order to be approved by the AWS Marketplace team. I suggest reviewing the documentation above or this AWS Marketplace SaaS Listing Process & Integration Guide.