How soon can a dog be groomed after neuter?

Neutered is the name of the process done to male dogs.

Which makes your question unclear.

You could be asking about at which age male puppies can be neutered.

Or you could be asking about how soon after giving birth a female dog can be spayed.

Different questions, different answers.

Spaying a dog that has given birth = Once the puppies are weaned.

Spaying or neutering puppies, the suggestion is between 4-6 months. Basically as close to, but prior to, the age of sexual maturity. I feel that neutering and spaying too young (6-8 weeks) may have adverse effects on the pup's "emotional" stability. Speaking from experience.

Neutering an adult male dog can happen anytime regardless of what's happening in any pregnancy the male dog has caused.