Some of that will come with experience, he'll learn to trust Graham.
I'm not worried too much about their passing game it really boils down to their defense. There are some big holes so they have to get pressure on Rodgers or else he's going to carve up the left side and the middle. With Kam out, the middle of the field is wide open and the linebackers didn't play very good last week. Williams on the left is basically the same as having Maxwell (who got lit up in Philly!) so he's going to get picked on. None of that matters though if they get pressure, sacks, hits, hurries, all of that can lead to mistakes.
Offensively they need to run the ball well. Chicago had a lot of success with Forte, and they average 5.7 yards per rush against GB as a whole. So fuck, they better get thr run going, control the clock and keep the ball out of Rogers hands. That's how they can win this game - run well and get a lot of pressure on Rodgers.