Is there any way to recover save data from an old hard drive after upgrading?

Months ago, I upgraded to a 2TB hard drive and made sure to upload all my saved data to the cloud so nothing was lost. However, I apparently forgot to download the data for Just Cause 3 onto my new drive, and when I played it for the first time in months yesterday, a brand new file started, which overwrote the one saved on the cloud. I still have my old hard drive, so all my old data should still be on there. Is there any way for me to extract that old save file and use it on my new drive or am I screwed?