Puppies can start socializing with other dogs safely depending largely on their vaccination status rather than just age. Here are the key guidelines:

• Puppies typically begin their vaccination series at about 6 to 8 weeks old, with full vaccination usually completed around 12 to 18 weeks of age.
• A puppy is considered fully vaccinated and safe to interact freely with other dogs about one week after their final round of shots, which is typically around 14 to 19 weeks old depending on the vaccine schedule.
• Before full vaccination, puppies should avoid contact with unvaccinated dogs or dogs whose vaccination status is unknown to prevent disease risk.
• Puppies can play with their littermates and vaccinated dogs in their household earlier than meeting unknown dogs outside.
• Socialization can begin earlier in a controlled way: puppies can be safely exposed visually or from a distance to other dogs and the environment before full vaccination. Puppy playgroups may allow interaction after one round of vaccinations but in clean, supervised settings.
• It’s important to ensure all dogs involved are up to date on vaccinations and healthy.
• Early socialization (starting as early as 3 weeks but ideally 7-8 weeks with some vaccinations) is crucial for proper behavioral development but must be balanced with the puppy's health safety.

So in summary, puppies can be around other vaccinated dogs at home before they finish their vaccines, and may start playing with other puppies after their first set of shots (around 8 weeks) in clean supervised environments. For broader socialization with unknown dogs, wait until your puppy is fully vaccinated, typically around 14 to 19 weeks of age and one week after the last shot.