We cannot restore cancelled orders. The best thing that you can do, is to copy the cancelled order in question.
Navigate to SALES > Orders in the left menu of the back office and select the order. You will be taken to its dashboard. Click Copy order at the right at the bottom of the screen. The order copy will be created as an offer, which can be converted by clicking Convert to order. You now have the option to set the order status to Paid and Shipped, just like with the original order.