What you call "social proofing" has a scientific name: allelomimetic behavior
There's an interesting article by Psychology Today that includes 2 videos that showcase the effect of learning from another dog vs. learning on their own:
One aspect of dog learning that often seems to be overlooked by the scientific community has to do with dogs modeling their activities on the behaviors that they observe in other dogs. This involves what scientists call allelomimetic behaviors. These are group-coordinated behaviors that depend upon an inborn inclination for dogs to want to be with other dogs, to follow their lead, and do the same thing. Puppies show tendencies to imitate the behaviors of others from an early age and this continues throughout their lives.
However, dogs learn generic behaviors like proper social interactions, how to react if a car approaches or how to walk down the stairs via allelomimetic behaviors. I doubt that befriending an individual human could be taught like that.
The better alternative would be befriending that dog directly. You have to take the dog's personality into account if you want to succeed. My personal experience is that:
Street dogs tend to be wary of people. All it takes is one bad experience like being lured by a person and then hit with a stick for a dog to become cautious. Street dogs tend to be especially wary of men, because they seem to attack dogs more often than women. If the dog is wary, the best approach is to ignore it. At first this may sound counter productive, but you have to give the dog time to approach you and trust that you won't attack it. As long as you follow it around, it won't relax and build trust.
Watch your body language! Many people get this wrong and actually scare dogs away when they want to approach them.
- Do not look the dog directly into the eyes. In dog language this is a warning sign.
- Don't smile and show your teeth. In dog language this is a sign of aggression.
- Don't bow your upper body down while keeping your legs straight. That way you tower over the dog and intimidate it. Instead either kneel or sit down to be at eye-level with the dog.
- Give the dog time to sniff you before you try touching it. The first move towards you must be done by the dog. You cannot force trust to develop, you have to wait for it to develop on it's own.
- Do not lift your hand over the head of the dog. Most people (especially children) always want to pet the head of an animal, without realizing that it takes trust to have your head touched. Start with petting the breast / front of the torso instead.
I find a small pocket mirror to be very handy for such situations. It allows you to watch the dog's body language without provoking it by directly looking at it. Look out for signs of stress or aggression as listed in this answer.
Involve the dog's nose. The nose plays a much bigger role in the life of a dog than that of a human. By having a treat with a strong smell in your hand (like a small piece of cheese or hotdog sausage), you can arouse this dog's interest in you much more than with visual clues like body language. You can start with throwing a treat in front of you (just outside your own reach) and looking away from him. Then hold the treat in your fist, but give it to him only after a few seconds. That makes you as person extremely interesting to this dog.
And last but not least, keep in mind that you cannot force friendship. All the tips I gave you are well-meant, but if the dog decides that it doesn't want to be friends with you, there's nothing you can do.
