If we are born with hearts of flesh that become stone at some point then prior to that point we should be able to choose to follow God on our own accord.
I am reminded of Paul's testimony:
Gal 1:14 And I was advancing in Judaism beyond many of my own age among my people, so extremely zealous was I for the traditions of my fathers.
Gal 1:15 But when he who had set me apart before I was born, and who called me by his grace,
Gal 1:16 was pleased to reveal his Son to me, in order that I might preach him among the Gentiles, I did not immediately consult with anyone;
Gal 1:17 nor did I go up to Jerusalem to those who were apostles before me, but I went away into Arabia, and returned again to Damascus. (ESV, emphasis mine)
Notice Paul is pointing out that God Himself is n charge of when he was able to see Christ for who He is and respond. We know Paul heard the Gospel prior to his trip to Damascus, and we can safely assume (IMO) that he probably heard it quite often.