Instead of attempting to use logic and reason to deduce a way to establish a valid justification for God (‘theos’) being just (‘dikaios’) in the light of suffering and evil, it may be more simple…
The following statement of Jesus in John 16:33 is key:
“In this world you will have trouble; but take heart, I have overcome the world.”
This beautiful and terrible world was always going to be both beautiful and terrible. Whatever time is, whether in terms of physics, metaphysics, science or theology, it necessarily entails process, opportunity, possibility and freedom.
On the one hand, God is not an absentee landlord, abandoning our space/time world to descend into chaos, but on the other hand, God is not a manipulative control-freak, exerting hands-on force upon the world, causing and desiring everything that happens in every and all senses of the word ’cause’. God cares. But this does not mean that God prevents every bad thing from happening.
Instead, we are given a promise that God will sort it out eventually, or indeed that in and through Jesus that sorting out has already been inaugurated. If Jesus is really risen from the dead, then God really has already begun to overcome the world with all its trouble.
This is a theodicy of hope.