Are you talking about media files or the page attachments?
If you mean media files, once you have the storage provider in place, just copy the original media library folders and files to S3 - just keep the same folder structure.
If you mean page attachments, you need to set the system to store files on file system - and then, once the file is requested, it will be copied to the S3 storage automatically. Or, you can save all the attachments to disk at once in System -> Files.