Advice for a Brand New Facilitator
If you are a social skills mentor with no prior experience with TTRPGs, this article contains my advice on how to get started.
My first advice: don't run it alone! See if you can find an experienced Storyteller (also called a DM) and ask them to run the initial campaign where you participate as a Player, learning through observation. If you don't know any Storytellers, my advice is to find out where your LGS (Local Game Store) is, as they will often have a “TTRPG Night” or “D&D Night” where you could likely meet experienced TTRPG Storytellers.
If collaborating with an experienced Storyteller isn't feasible, here's my next suggestion. Your first TTRPG should be 5th Edition Dungeons and Dragons. 5th Edition D&D is by far the most popular TTRPG out there, and has two main benefits. First, there are TONS of pre-made adventure modules for D&D, which remove most of the “prep work” that a Storyteller does between the sessions to prepare for the next session. After all, you don't need to design the obstacles in the dragon's lair if the adventure has already designed them for you. Second, D&D has some of the easiest rules to learn of any TTRPG. There's no need to overwhelm yourself with a more nuanced and in-depth TTRPG if it's your first time running one. I still advise finding a group to participate at least once as a player, as it will really help you get an idea of what is in store. Barring that, go watch an episode of Critical Role or Dimension 20. Just be aware that those are PROFESSIONAL TTRPG groups with years of experience and actual monetary budgets. That is their job, and so don't accurately reflect what the typical TTRPG experience is like, but at least gives you an idea of the structure and nature of a TTRPG.
There is another possibility: TTRPGs are massively popular with autistic individuals already. It's possible that one of your participants is already experienced with TTRPGs. You might be able to “team up with them” in a shared role of Storyteller. This relates to a long-term goal of groups such as this. Ideally, your Players will gain enough experience and social confidence that they can take over the role of Storyteller and help guide other, newer players along similar development tracks.