Subscription has not yet started
Navigate to the subscription you wish to change and select the pencil icon beside 'Start'. You can then select any future date.
Select the new date, press Preview changes, and then confirm when you are happy by pressing Change start date.
That's all there is to it. Move-in info will now be sent to the customer on the new date, and payments will be collected from this new date.
Subscription already started
If the subscription has already started it is not possible to change the move-in date. You will need to cancel the subscription and recreate with the new date.