Here’s the catechism teaching on a couple of aspects where it’s recognized that man’s will is involved, even as God’s initiative is essential:
1731 Freedom is the power, rooted in reason and will, to act or not to act, to do this or that, and so to perform deliberate actions on one’s own responsibility. By free will one shapes one’s own life. Human freedom is a force for growth and maturity in truth and goodness; it attains its perfection when directed toward God, our beatitude.
1732 As long as freedom has not bound itself definitively to its ultimate good which is God, there is the possibility of choosing between good and evil, and thus of growing in perfection or of failing and sinning. This freedom characterizes properly human acts. It is the basis of praise or blame, merit or reproach.
1993 Justification establishes cooperation between God’s grace and man’s freedom. On man’s part it is expressed by the assent of faith to the Word of God, which invites him to conversion, and in the cooperation of charity with the prompting of the Holy Spirit who precedes and preserves his assent:
When God touches man’s heart through the illumination of the Holy Spirit,
man himself is not inactive while receiving that inspiration, since he could reject it; and yet, without God’s grace, he cannot by his own free will move himself toward justice in God’s sight. 42
Augustine produced a huge amount of writings, a great deal of which was the result of his battle against Pelagianism where he understandingly emphasized the role of grace. But here’s a very famous quote from His later years, from Sermo 169:
"But he who made you without your consent does not justify you without your consent. He made you without your knowledge, but He does not justify you without you willing it.”
And the catechism again, this time on predestination:
600 To God, all moments of time are present in their immediacy. When therefore he establishes his eternal plan of “predestination”, he includes in it each person’s free response to his grace: "In this city, in fact, both Herod and Pontius Pilate, with the Gentiles and the peoples of Israel, gathered together against your holy servant Jesus, whom you anointed, to do whatever your hand and your plan had predestined to take place."395 For the sake of accomplishing his plan of salvation, God permitted the acts that flowed from their blindness.396
"He died for our sins in accordance with the Scriptures"
1037 God predestines no one to go to hell;618 for this, a willful turning away from God (a mortal sin) is necessary, and persistence in it until the end. In the Eucharistic liturgy and in the daily prayers of her faithful, the Church implores the mercy of God, who does not want “any to perish, but all to come to repentance”:619