Okay, loose strategy for mission(note, somewhat guessing on Provincial actions):
Now
-Survey Land
Turn 1:
-If Survey Land finds a Redhill deposit:
--State Main - Build Iron Mine (Econ 9->?(unknown large bonus, but should stop at cap and overflow anyway), Stability 1->0, Mysticism 3->4, Art 7->8)
--State Secondary - Change Policy - Balanced
--State Secondary - Build Watchtowers - Southshore(Econ ?->?)
--Province Law - Expand Economy (Art 7->11 Econ overflow)
--Province Secondary 1 - Build Watchtowers - Southshore/Study Stars
--Province Secondary 2 - Improve Annual Festival
--Province Secondary 3 - Improve Annual Festival x2 (Econ ?->?, Art 11->12, Stability 0->1)
From here, it's simply doing Study Metal on Turn 2, and Study Tailings on Turn 3, if the provinces don't Study Health on Turn 2, we'll have to do it manually and accept that Turn 3 has no flexibility left.
-If Survey Land finds a wilderness deposit instead:
--State Main - Study Metal(Econ 9->8, Myst 3->1, Stability 1->0)
--State Secondary - Change Policy - Balanced
--State Secondary - New Settlement
--Province Law - Expand Economy(Econ 8->12)
--Province Secondary 1 - Study Health
--Province Secondary 2 - Study Health x2(Econ 12->11)
--Province Secondary 3 - Build Watchtowers - Southshore(Econ 11->10
From here, it's simply doing the Mine on Turn 2, but depending on specific province actions we might not be able to do the last Study until turn 3 due to lacking Mysticism until the Mine is built. We'll have to do a Turn 2 Grand Sacrifice or Festival instead.
Still a lot of variables, but
@Academia Nut can we assume that the provinces will try to Main a Study Health when we're studying either Metal or Tailings in order to advance the challenge?
Barring something being urgent in their view, like Southshore taking a defense building.