People like to talk about the elasticity or compute, but startup is not free (or even cheap in most cases).
OP is probably talking about an x1e.32xlarge. According to Daniel Vassalo's S3 benchmark [1], it can do about 2.7GB/sec.
So your 4TB DB might take ~30min to fetch.
Bandwidth is free, you'd pay $2 for the 30 min of compute, and some fractions of pennies for the few hundred S3 requests.
[1]: https://github.com/dvassallo/s3-benchmark
People like to talk about the elasticity or compute, but startup is not free (or even cheap in most cases).