I have done data recovery on similar cases. By default Windows will do a fast format so the data continues to exist on the disk if not overwritten by the new files saved on the disk by the windows setup.
A recovery like that can only be done using paid software like GetDataBack, R-studio, etc. the programs can be downloaded to check what they can recover by previewing the files then you decide to buy them or not.
You should install the HDD as second drive in another machine to avoid writing new data to the disk because it reduces the chance of recovering the files. During the recovery process the files recovered need to be saved to a different HDD.
If you don't have another computer to install the recovery programs GetDataBack provides a Linux live CD that can be used to do the recovery without using the new Windows install.