You say God cannot cause people not to believe. He doesn't need to, they are already in a state of unbelief! However, He can change a person's heart to believe when they hear the preached word. When that happens, it is not a work of man - it is a work of God himself!
Now tell me if you think this is true.....
They can't be in a state of unbelief unless they first have something to not believe ergo, God always initiates with grace and truth and the Devil follows closely behind with his "brand of truth". I strongly suspect many people have forgotten or were completely unaware of their first encounter with the Lord because they were very young. But He is there from the get go. The Spirit is in the world convincing people of righteousness, sin and judgment. Needless to say, the Devil's doing his own version of convincing as well.
Did the devil change your heart to not believe or did you decide that for yourself? You came into this world knowing neither truth nor lies, you heard both from somewhere. If the "devil didn't make you do it", why would you think God made you believe the truth? Why is it so hard to accept your decisions between truth and error are your decisions? It doesn't in anyway take away from God's power or glory as it was by means of His grace and mercy you heard the truth in the first place and it was His power that saved you based on His own determination to save believers. It was His design that gave you the capacity to use your will for limited self determination.
God has never given our volition the power to create reality so how could our volition be responsible for changing our reality simply because we use it as God tells us to do? "repent and believe", "believe on the Lord Jesus Christ" "choose you this day" etc. You weren't living in a coma all your life until the Gospel suddenly sprang into your heart. You have been making decisions for and against the Lord all your life.