Will people seek God on their own without God first moving?
No. Mankind will never, of his own volition, go looking for God; it is contrary to our human makeup. As with Adam and Eve, who hid in the garden rather than running to meet Him, God must make the first move. Yet the work of the cross was sufficient for everybody, not for a preselected few.
Les teaches that this principle has never changed since the garden. When Adam and Eve sinned and made their fig leaves, they did not run to meet the Lord in the evening; they hid, and God had to find them. In the same way, mankind will never of his own volition go looking for God, because it is contrary to our makeup. God has to make the first move. Les is careful to add that this does not mean God has forgotten some and, by what is called extreme Calvinism, already picked out who He will save and who He won't; he does not agree with that one whit, because the work of the cross was sufficient for everybody. He illustrates this with the door to the sheepfold in John's Gospel, chapter 10: that door is not located where it ostracizes some people, but at ground level, not beyond the reach of anybody. Nevertheless, it still has to begin with God.