Full explanation
This question rests on a common mix-up, so let us clear it first. Le God Mode is not a scatter-triggered round you grind toward in the base game. It is a Feature Buy that costs 50x your bet and guarantees at least 6 Mystery symbols on every spin. There is no scatter count that unlocks it for free.
The scatter-triggered rounds are the other two: 3 scatters for Bolt & Run, 4 scatters for Myth-Taken Identity. Hacksaw does not publish the exact probability of landing those, but as bonus triggers on a medium-volatility slot they are uncommon, which is normal.
So if you specifically want the guaranteed-Mystery experience of Le God Mode, the buy is the route, assuming your casino offers buys (some regions block them). Notably, FS scatters cannot land during Le God Mode, so you are paying for guaranteed Mystery frequency rather than a path back into the scatter rounds.
Practical answer: there is no "scatter probability for Le God Mode" to calculate, because that is not how you get there.
If you want guaranteed Mystery frequency
Because Le God Mode is a buy rather than a scatter goal, the only way to guarantee it is the 50x purchase, where your casino allows buys. You are paying for a mode that puts at least 6 Mystery symbols on every spin, at the trade-off that FS scatters cannot land while you are in it.
If buys are blocked in your region, Le God Mode simply is not available to you on demand, and no amount of scatter collecting unlocks it. In that case the scatter-triggered rounds, Bolt & Run and Myth-Taken Identity, are your natural bonus path instead.
Because the studio has not published the exact scatter odds, treat Le God Mode as a rare natural event or simply buy it when it is offered. The buy exists precisely so you do not have to wait on a low-probability collection. Whichever route you take, do not size your bankroll around the assumption that the scatters will land for free.