My coworker Yuvaraj and I were over thinking this WAY to much. I finally figured out how to do a full restore on a clean Veeam installation right out of the box.
Add your S3 repository
Home ==> Backup Infrastructure ==> External Repositories
Confirm you have a valid bucket name, access key, and master key.
Import the backups from the S3 bucket into the Veeam
When the inventory scan of the S3 bucket is completed you will see the restore points in home menu.
Home ==> Backups ==> Object Storage (Imported)
How a restore from an S3 object storage repository looks like