S3 bucket put operation SNS notification

Instead of using SNS, why not use SQS as the notification path? You'll still get (say) nine notifications but you can trigger a build at a specific time during the week and then get all nine notifications from SQS at the same time.

If you can filter by the by the prefix and suffix of the object name to only match one of the nine objects then you may be able to (in effect) ignore the other eight https://docs.aws.amazon.com/AmazonS3/latest/userguide/notification-how-to-filtering.html

Otherwise, if all nine objects will be uploaded within a 15 minute period then a lambda function would suit this use case - either send an email when the first object is uploaded to the bucket and do nothing for objects 2 to 9; or do nothing for objects 1 to 8 and send an email when object 9 appears.

If the time from first to last could be more than 15 minutes then consider using a step function.