It's probably done by skunks. Here's more: https://extension.umd.edu/hgic/topics/skunks
The good news is that fall is the premier time to overseed your lawn anyway. And the skunk has already worked up the soil for you. Here's how to renovate your lawn: https://extension.umd.edu/hgic/topics/lawn-renovation-and-overseeding
Skunks would be a first for us here in 56 years! There's no place on our property that would provide the home you described. Is there some way to prevent or discourage them from digging up the sod?
We have been receiving several questions about turf being dug up this time of year.
As mentioned above skunks, raccoons, possibly opossum and fox can do this type of damage. https://extension.umd.edu/hgic/topics/lawn-wildlife-problems
Skunks and other critters may dig in the turf looking for soil insects including earthworms, grubs, and other soil larvae. The ground is soft and soil insects are closer to the surface of the soil this time of year. They will move on.
You can look in the area for grubs. Keep in mind that a few grubs in the lawn is normal and healthy. Lawns usually grow back their roots faster than grubs can eat them.
When grubs feed on turfgrass roots, the turf can be rolled back like a carpet. Here is our page on grubs http://extension.umd.edu/hgic/topics/grubs-lawns
Repellents are not effective and grub control products should only be applied to a lawn if the grubs are feeding on turfgrass roots. The critter will just feed on another food source like earthworms.
There are no easy answers when it comes to wildlife control. Be sure to eliminate all sources of outdoor food including cat and dog food, bird feeders, exposed garbage cans and compost piles. You may be able reposition chunks of turf and step on them to ensure root contact. Reseed heavily damaged areas. http://extension.umd.edu/hgic/topics/skunks
Here is a link on seeding http://extension.umd.edu/hgic/topics/seedingsodding-lawns