Here is my reply, slightly revised, to a question on a discussion list. Perhaps it might be useful to someone somewhere.
A person asked about God “working on the heart of all living souls at some point in their life, either through divine intervention or through creational DNA.” God does manifest himself in creation. The universe points to God, Psa 19.1-4. Man is answerable to God for this knowledge, which man generally represses in order to worship idols. So Rom 1.
Ecclesiastes seems also to point to an emptiness within man without God’s knowledge. Some understand Eccl 3.11 in this way: “he has put eternity into man’s heart.” He is created with an inherent need for God. Man is going to worship something. That seems to be evident that religion is present in all cultures. Even in the USSR, man found some focus of veneration. Perhaps this is what is meant by “creational DNA.” I’ve never heard that term, however.
People often reach points of greater receptivity in their lives to the gospel message, than in other moments. I don’t know, however, that we could call these moments of divine intervention. If God wants all to be saved, that means he would have to intervene miraculously for everyone, in order to be fair.
Acts 8, 9, and 10 seem to point against God intervening miraculously (and without human participation) to convert man. In the NT, no one is saved without another person proclaiming the gospel: Philip to the eunuch; Ananias to Saul; Peter to Cornelius and his family. Never is a person saved by some direct operation, be it angelic or Spiritual, apart from the proclamation of the gospel. The Lord opened Lydia’s heart when she listened to the gospel, Acts 16.14.
God said he would save the lost through the work of the church. This is our mission.