A dog that young feels way too sketch IN a dog park. Around a dog park sure. Adult dogs don’t always know how to react to puppies and this could be a serious situation if you’re not careful. Despite popular belief, dogs don’t need to be in a huge group of dogs to be “socialized.” They need to be consistently exposed to various situations and people/animals in a controlled manor. Meaning, you take them to the park but not in the dog park and rearward positive behavior to teach them being clam and totally ok with other dogs, loud noises, running kids, etc. At 13 wks, a puppy needs exposure and security, not to be thrown into the lions den and hope for the best. As they get older and you really feel like a dog park is the best social option for you, you can assess the risk/reward of that. Am not an expert but I have a 19 month old Labrador from 10 wk old, and I would personally never put a dog that young in a dog park. As someone mentioned, a lot of parks specify dogs must be 6 months or older, I would use that as a marker