Besides the scriptures, which I do believe to be accurate, I have seen evidence in real life. A very good (non-Christian) friend of mine who is spiritually into Buddhism and eastern practices has had Christ intervene in her life on at least two occasions of which I am aware and I'm sure there are many more. She had a very hard childhood, has gone through several messed up relationships. On one occasion she was camping at a meditation retreat when in the middle of the night she was awakened by someone saying," Get out now!". She immediately fled her tent and in an instant a huge tree fell directly on it. No one else was there, but her life was saved. On another occasion she was walking alone at the beach and feeling very lonely on her birthday when she said it was as if the 23rd was being spoken to her mind and it brought her comfort in her loneliness. You cannot tell me (well you can) that God is not at work in her life drawing her to Himself, yet, at this point she still rejects Jesus Christ.
My own father has had numerous occasions that I see he has experienced God intervening and protecting him to give him opportunity to repent and be saved. He is now 98 years old and likes to talk about God and Jesus sometimes, but still rejects Jesus as his Savior.
These are only two people, but I have no reason to doubt God's ability and desire to work in every person's life.