Personally I think the main issue that you're going to have is not so much the ingress rate to Amazon's S3 service but more so the network egress rate from Google's Network. Even if you enabled the S3 Transfer Acceleration service, you'll still be restricted by the egress speed of Google's Network.
There are other services that you can set up which might assist in speeding up the process. Perhaps look into one of the Interconnect solutions which allow you to set up fast links between networks. The easiest solution to set up is the Cloud VPN solution which could allow you to set up a fast uplink between an AWS and Google Network (1.5-3 Gbps for each tunnel).
Otherwise from your data requirements the transfer of 3,000 GB isn't a terrible amount of data and setting up a Cloud server to transfer data over the space of a week isn't too bad. You might find that by the time you set up another solution it may have been easier in the first place to just spin up a machine and let it run for a week.