My dog “Puppy” was hit by a car when I was a kid. It only damaged his right front paw . We didn’t have money for a vet, so we bandaged it and he dragged it around for a week. The neighbor lady couldn’t stand it so she paid the vet to take the leg off, leaving just a short stump. Puppy adapted right away and hopped around on three legs several more years.
Bigger dog breeds, unfortunately, are completely another matter. A large dog is carrying around a lot more weight on those legs and needs time to build strength in the opposite good leg. It can happen, depending on the dog's temperament, persistence and patience. But more often than not, these things don't end well.