Running out of space will cause problems with anything. I just went to edit a config file on my Docker VM, and not only would it not write the changes, but it somehow deleted the original file at the same time! Yep, root volume was full (I really need better monitoring/alerting...), but after cleaning out some unneeded Docker build cache I was able to restore the file from yesterday's backup and all was well.
Moral of the story - cloud isn't the problem, it's lack of storage. It's always lack of storage. ;)
Fastest "normal" way would be write it to a USB 3 drive on machine 1, read from drive later on machine 2. An SSD would be best. Even with having to do the write and read in two phases, I'd still expect it to be faster than a 1G network.
(Less normal ways would be things like Thundrerbolt SSDs, 10G or 40G ethernet for direct transfer, etc. But if you have that kind of tech already in place, then you're not asking. ;)