If the "remote server" is Azure, the target throughput is 0.5gbps ... for each large blob (of which this leak includes many). It seems pretty likely you'll be able to download at a few gigabits per second if your local connectivity allows.
We're talking about exfiltrating data from incorrect permissions on Azure, so it's not an if. It's a given for the situation in the article that we're discussing in this thread.
that's not quite true. the article discusses a transfer from Azure to Github. The article does not say where the files are currently hosted, besides being publicly available on Github. It's probably Azure, but it could easily also be whatever Github use
38 terabytes = 304 terabits.
304 terabits / 1 gigabit/second = 304,000 seconds
304,000 seconds =~ 84 hours. Add 20% for not pegging the line the whole time and the limits of 1gbps ethernet, and perhaps 100 hours is reasonable.