Regarding the OP’s question, we have to remember that God gave us a free will, so it is up to us to use it properly and cooperate with God in order to do good. We sinners are responsible for the evil in the world, though God even uses the bad to bring about good. All things are possible for God.
Almost there.
We are free moral agents. But only as free to live as our nature, personality, opportunities, desires, etc. allow us–all which God gives to us.
Therefore, I prefer to not think of it as cooperating with God, but rather, living out His plan and purpose for our lives. (whether we do good or evil)
Consider the Pharaoh who oppressed the Hebrews. Yes, the Bible is very clear when it says,
“Pharaoh hardened his heart.” Yet it is equally clear when it also says,
“God hardened Pharaoh’s heart.”
Moreover, there are several places scattered throughout the Bible which pull back the curtain and reveal God backstage directing the moves of this historical character.
Exodus1:8 “Now there arose up a new king over Egypt, which knew not Joseph.” (enter stage right)

The following verses tell us this new Pharaoh oppressed the Hebrews because they were greater in number.
The Psalmist points out God’s role in this:
Psalm 105:24 “[YHWH] increased his people greatly; and made them stronger than their enemies. He turned [the Egyptians] heart to hate his people, to deal subtilly with his servants.”
Likewise, Moses attributes Pharaoh’s activity to God’s plan and purpose for him.
Paul quotes Moses in
Romans 9:17 "the scripture saith unto Pharaoh, Even for this same purpose have I [YHWH] raised thee up.”
The Bible clearly demonstrates that God didn’t merely permit an entire nation to hate and oppress his people, He
raised it up. Israel’s suffering and
“cruel bondage” (Ex 6:9) was God’s perfect will and personal activity.
Cooperation isn’t quite accurate because though our will is not coerced into action, we will to do only what God willed for us that we should do.
To think otherwise is evil boasting.
James 4:13 “Come now, you who say, “Today or tomorrow we will go into such and such a town and spend a year there and trade and make a profit”— yet you do not know what tomorrow will bring. What is your life? For you are a mist that appears for a little time and then vanishes. Instead you ought to say, “If the Lord wills, we will live and do this or that.” As it is, you boast in your arrogance. All such boasting is evil.”
Let me add that, although God controls evil, your remarks concerning His love and charity and goodness shine remarkably in all His acts whether working good or evil in His creatures. Hence, the hope of Job in the face of severe adversity:
"The Lord gave, and the Lord has taken away; blessed be the name of the Lord.”
"Shall we receive good from God, and shall we not receive evil?”