Does the hardened criminal need more grace than the little girl to come to know Jesus as savior? To answer this, we must clarify grace.
Grace is receiving goodness that you did not deserve. It is expressed by God for salvation through the death of His Son. The same death that pays for the sins of a little girl also pays for the sins of the hardened criminal. There is no less grace or no more grace that anyone could ever receive for salvation. Each receives the same grace of God for salvation.
Does it take God a greater effort to save the hardened criminal? The Almighty God has infinite power. He can work on everyone in the world at the same time without breaking a sweat. The question will never be whether we tested the strength of God to be saved. The question is: "Is it harder for an individual to give their life to Christ after being a hardened criminal?" The answer to that must be "yes."
Salvation involves trusting in the Lord. That trust means you put your life in His hands. The little girl may have her whole life in others hands. She has been taken care of by her parents for food, shelter and clothing. They have taken her to the doctor when she was sick. They have driven her to the things that she has wanted or needed. She has always trusted in someone. It is easier for her to make the connection between trusting someone and trusting the Someone. She trusts those who tell her to do so.
The hardened criminal has lived trying to make it on his own. He has learned that you can't really trust anyone. He has learned that "number one" has to be placed at the top of every list when dividing the spoils. He struggles to give his life to Christ because trust is a real issue for him. He is more likely to adopt a religion of works than one of grace. He understands doing. He does not understand having it done for you. He has to overcome huge obstacles to come to know Christ.
Many people think they have some living to do before they can come to know Christ. There are some sins they have not yet committed to their fulness. They want to do this before they come to Christ. They do not realize that they are laying a foundation which will prevent them from ever coming to know Christ. It will become almost impossible for them to trust in Christ once these patterns become a part of their lives.
This is why the Bible says that today is the day of salvation. It is never tomorrow. There will be time tomorrow is the song sung in hell. We all exist for an eternity but some will not want to.
Thank God for His grace.