Let me first answer a question that wasn't asked: Do we really need more junior positions? Or should we realize that there are a lot of junior positions where we can experiment with our newly acquired Service Design skills? To me, you can work as a junior UX designer, and still create a lot of valuable work where you use your Service Design skills. 

In some way it's our responsability as people passionated in Service Design to bring it in places where its maybe not known yet instead of waiting that we get invited.

Now to come back to the first question: "How can we get more junior Service Design positions?" here a few thoughts. In other domains like marketing, graphic design, UX, some of the best places to find junior positions are agencies. Agencies need a lot of cheap talent to survive. And junior level staff is exactly that. So in order to be able to have more junior level job positions in Service Design we might need to have more Service Design agencies. 

Also the more Service Design agencies there will be out there, the more institutions and organizations will realize that they need service designers.

Check out all the questions about Service Design as a career.