AWS egress can go as low as $0.05 with >150TB volume. It takes $10k/month spend to get to this threshold. This is advertised on their website at https://aws.amazon.com/s3/pricing.
Before contacting sales for a higher discount, I want to know what volume discounts you or your company are getting. Is $0.02 or $0.01 possible? Is there a monthly commitment/threshold? If not AWS, is this is possible with Azure/GCP?