Look for breeders that raise their pups with the Puppy Culture or Avi Dog programs.
Your best bet is to find a breeder who keeps the dogs to at least 8.5 weeks of age and starts socialization with kids, adults, lots of environmental enhancement such as moving the rearing box to different rooms in the house, introduces different toys periodically, does early neurological stimulation that helps to create a more resilient adult etc, then continue the pup's socialization. The goal is to have all positive experiences in the first 16 weeks of the pup's life. Meet at least 100 different people, visit different indoor and outdoor locations, different surfaces, sounds, sights, modes of transport, meet other dogs that are properly socialized and friendly (even if the final vaccinations have not yet been done), plus expose the dog to any environments you anticipate s/he will be exposed to during her lifetime. etc After the 16 weeks, it is important to maintain all this but not as intensive.
You can start the basic training (sit, eye contact, leave it, nose targeting etc) as young as when you bring the pup home. Some clicker trainers start the pups at 4 weeks as soon as they can hear. But be careful to let your pup be a pup! Your dog is a dog first, family member second and service dog third. If you plan to do other things (like compete in sports), train those later if the service dog is the primary focus. Avoid asking too much of your dog as they can burn out. Working as a service dog for one person is a full-time job for most dogs. Some dogs, like diabetic and seizure alert dogs, are on 24/7 so make sure to give the dog time away from work on a regular basis.
Know that no service dog is ready to work in public until after about 18 months of age. If someone is trying to sell you a "trained" service dog that is younger than that, especially a 12 to 16 week old pup, then run away! Pups of this age do not have the social, emotional or physical maturity or reliability to handle this job, even if they can already detect blood sugar highs and lows. They have not been trained to work in public. Plus it's not fair to the developing pup to put that level of responsibility on him or her.
You can adopt an adult dog and train it to be a medical detection dog. They do not need to be raised using their nose to learn the task. Dogs know how to use their nose and if they have a bond with you, they can easily learn how to do medical alerts of all kinds. Avoid short-nosed breeds for the job just because they often have health issues due to the short nose structure or heart issues.
Here is a FREE e-book that helps you to select a service dog from various sources.