Is there a way to use the Crop tool non-destructively in Photoshop?

By selecting your crop tool in the toolbar. In the top menu bar you'll find the cropping options and you'll find the Delete option selected so unselect it and select Hide instead. This will not delete the rest of your image, it will just hide it. If you want to get back to the full image you can just go the top menu and choose Image and then choose Reveal All.