Develop a lightweight application using App Engine that continuously monitors the Cloud Storage bucket for new files and initiates the training job upon detection, ensuring immediate response to new data.

Configure Cloud Scheduler to periodically check the Cloud Storage bucket for new files. If new files are detected since the last check, it triggers the training job on GKE. This approach ensures regular checks but may introduce delays.

Set up a Cloud Storage trigger to publish a notification to a Pub/Sub topic whenever a new file is added. Use a Pub/Sub-triggered Cloud Function to launch the training job on GKE, providing an event-driven and scalable solution.

Utilize Dataflow to process and save files in Cloud Storage, with a subsequent step to automatically start the training job on GKE. This method integrates data processing and model training but may add complexity.

Combine both the event-driven approach using Pub/Sub and Cloud Functions for immediate response and the scheduled checks with Cloud Scheduler as a fallback mechanism to ensure no data is missed.