The question about how the sovereignty of God relates to the responsibility of man is an old one.  In His book, Evangelism and the Sovereignty of God, J. I. Packer addresses how God’s sovereignty relates to our responsibility in proclaiming the gospel to unbelievers.

There is abroad today a widespread suspicion that a robust faith in the absolute sovereignty of God is bound to undermine any adequate sense of human responsibility. Such a faith is thought to be dangerous to spiritual health because it breeds a habit of complacent inertia. In particular, it is thought to paralyse evangelism by robbing one both of the motive to evangelize and of the message to evangelize with. The supposition seems to be that you cannot evangelize effectively unless you are prepared to pretend while you are doing it, that the doctrine of divine sovereignty is not true. I shall try to make it evident that this is nonsense. I shall try to show further that, so far from inhibiting evangelism, faith in the sovereignty of God’s government and grace is the only thing that can sustain it, for it is the only thing that can give us the resilience that we need if we are to evangelize boldly and persistently, and not be daunted by temporary setbacks. So far from being weakened by this faith, therefore, evangelism will inevitably be weak and lack staying power without it.