When order 66 was issued, thousands of Jedi died within only a few hours.
The effect on the force was powerful; we see Yoda physically react like Obi-Wan did in A New Hope. Now, imagine the effect this has on survivors.
We know how conflicted Kanan and Asohka became, so if there were other survivors, who knows the effect that may have had on them.
Imagine, Snoke is a padawan during the clone wars. Order 66 is enacted, and his master is killed. A blind rage and confusion comes over him.
He abandons the Jedi way and goes off into unexplored space to bide his time.
The key to all of this is that Snoke, by rights, is the last living Jedi of the republic era. Luke never had full Jedi training.
He created a successor order, but what legitimacy did it have to be the real successor to the Jedi of old?
We know Snoke isn't a sith; maybe he considers himself, in his own twisted way, to be the last legitimate heir of the Jedi order.