I am not aware of any solution from the AWS side, but unless you have a special reason not to use gsutil or other Google solution, you may consider using Google Cloud Storage Transfer Service instead. This service is recommended when transferring data from Amazon S3 buckets.
Compared with simply using gsutil, or other CLI tools out there, Google Cloud Storage Transfer has several nice features like the possibility to schedule one-time or recurring transfers, where you can use advanced filters. Also, you can indicate if you want the source objects to be deleted after transferring them, and even synchronize the destination bucket with the source one, deleting existing objects if they don't have a corresponding object in the source.
You can schedule transfers from the GCP Console or using the XML and JSON API.