Increase the Cloud Function's timeout to nine minutes.

Configure the sender application to publish the outgoing emails in a message to a Pub/Sub topic. Update the Cloud Function configuration to consume the Pub/Sub queue.

Configure the sender application to write emails to Memorystore and then trigger the Cloud Function. When the function is triggered, it reads the email details from Memorystore and sends them to the email service.

Configure the sender application to retry the execution of the Cloud Function every one second if a request fails.