God must draw people to Christ (John 6:44), and "give them repentance to the acknowledging of the truth" (2 Timothy 2:25), and convict them of sin, righteousness and judgment (John 16:8) but, having done these things, the individual person is left to choose how to respond to all that God has done in making it possible for them to respond to the Gospel.
Even before salvation was accomplished, the Bible notes people who were righteous:
Matthew 1:19
19 And Joseph her husband, being a righteous man...
Luke 2:25
25 And there was a man in Jerusalem whose name was Simeon; and this man was righteous and devout, looking for the consolation of Israel; and the Holy Spirit was upon him.
Luke 23:50-51
50 And a man named Joseph, who was a member of the Council, a good and righteous man
51 (he had not consented to their plan and action), a man from Arimathea, a city of the Jews, who was waiting for the kingdom of God;
Acts 10:22
22 They said, "Cornelius, a centurion, a righteous and God-fearing man well spoken of by the entire nation of the Jews, was divinely directed by a holy angel to send for you to come to his house and hear a message from you."
Luke 2:36-37
36 And there was a prophetess, Anna the daughter of Phanuel, of the tribe of Asher. She was advanced in years and had lived with her husband seven years after her marriage,
37 and then as a widow to the age of eighty-four. She never left the temple, serving night and day with fastings and prayers.
These passages must temper how you understand passages like Romans 3:10-11, or Ephesians 2:1. In general, people don't seek after God; but there are still instances where this isn't so, where there are exceptions to the rule. Be careful, then, not to say more than the Bible does, overstating things as Calvinism's TULIP does.