One of the easiest ways to find Corgi puppies at local rescues is to search Petfinder for adoptable Corgis in your area. You can also look for a rescue that focuses specifically on Corgis and ask if there are puppies available.
Purebred dogs are available for adoption at many local rescues, but young puppies are usually less common. Adult dogs are more commonly available, so it may be a good idea to be flexible on the dog's age. Adolescent dogs and young adults often end up in rescues. Since Corgis are a high-energy working breed, even senior Corgis can still be active and fun companions.
Breed-specific rescues may be more likely to get Corgi puppies than all-breed rescues. To find Corgi rescues near you, start with the American Kennel Club Rescue Network's contact list. Call or email the organizations listed and ask them for local contacts. You can also try contacting your state or regional breed club. Responsible Corgi breeders might also be able to suggest rescues in your area.
Corgi puppies may be adopted from all-breed shelters quickly, so it may be a good idea to visit the shelter regularly in-person as well as checking online. Some shelter staff may be willing to write down what kind of puppy you are looking for and call you if a dog fitting that description arrives, but some may be too busy to do this.