There is only one condition to be able to safely retrieve your progress.

Players must be logged in to iCloud previously in order to be able to restore progress.

In the "Progress" tab you can find a switch you can toggle on or off to activate the save progress feature. Be sure to be previously logged in to your iCloud account before activating this feature!

If you were logged in to your iCloud account previously and had the Save Progress feature activated on the Progress tab, all you have to do to be able to restore your progress, is load the same iCloud account you previously had your progress linked to!