Ideally, all this data would have been already backed up to AWS (or your provider of choice) by the time your primary service failed, so all your have to do is spin up your backup server and your data would be waiting for you.
(Looks like HN does just this: https://news.ycombinator.com/item?id=32032316 )
Sure, though the solution where you back up the data probably won't be the same one where the new live DB will actually run, so some data transfer/IO will still be needed.
The S3 buckets where HN is backed up to could themselves be constantly copied to other S3 buckets which could be the buckets directly used by an EC2 instance, were it ever needed in case of emergency.
That would avoid on-demand data transfer from the backup S3 buckets themselves at the time of failure.
The backup S3 buckets could also be periodically copied to Glacier for long-term storage.
That's for an all-AWS backup solution. Of course you could do this with (for example) another datacenter and tapes, if you wanted to... or another cloud provider.