The requirement is for immediate processing of uploaded videos and prompt notification to users. According to AWS best practices for event-driven architectures, using S3 event notifications to trigger a Lambda function upon an object creation (upload) is the optimal solution for real-time processing. Lambda can process the file as soon as it is uploaded, ensuring low latency. Once processing is complete, Lambda can save the processed file back to S3 and use Amazon SNS to notify the user.

This approach uses managed services with minimal operational overhead, is scalable, and ensures event-driven processing with instant user feedback. AWS Amplify primarily facilitates application development and hosting but does not natively provide direct push notification support for this backend workflow; instead, SNS is designed for such notification scenarios.

Reference Extract from AWS Documentation / Study Guide:

"Amazon S3 can publish events to AWS Lambda when objects are created. AWS Lambda runs code in response to events and can interact with other AWS services. Amazon SNS is a flexible, fully managed pub/sub messaging and mobile notifications service for coordinating the delivery of messages to subscribing endpoints and clients."

Source: AWS Certified Solutions Architect – Official Study Guide, Event-driven Architectures section; AWS Lambda Developer Guide (S3 triggers); Amazon SNS User Guide.