Janean,
compare Romans 10 with Billy Graham's words.
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v. 8 But what does it say? The word is near you, in your mouth and in your heart(that is, the word of faith that we proclaim); 9 because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. 10 For with the heart one believes and is justified, and with the mouth one confesses and is saved. 11 For the Scripture says, Everyone who believes in him will not be put to shame.12 For there is no distinction between Jew and Greek; the same Lord is Lord of all, bestowing his riches on all who call on him. 13 For everyone who calls on the name of the Lord will be saved.

14 But how are they to call on him in whom they have not believed? And how are they to believe in him of whom they have never heard? And how are they to hear without someone preaching? 15 And how are they to preach unless they are sent? As it is written, How beautiful are the feet of those who preach the good news! 16 But they have not all obeyed the gospel. For Isaiah says, Lord, who has believed what he has heard from us? 17 So faith comes from hearing, and hearing through the word of Christ.

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Janean: But one thing what I struggle with - what doesn't makes sense to me - is that one can come to God without having known about Jesus.
From this passage of Scripture, they can't because faith comes by hearing the gospel and believing it.
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So then I think of Romans 1:19-20 which sounds like men have no excuse about God (even though they've never heard the gospel - never heard about the Bible,God, Jesus) so that has made me think that there is some "chance" for salvation for the person who has never heard of Jesus (like Billy G. just explained).
Well there is enough evidence in creation to show that God exists and to convict men and women of their sin, but not enough light for salvation. For that we need special revelation. Since God is Sovereign, He has no problem gettting the gospel to His elect wherever they are so they can hear and believe. He also commands us to take the Gospel to the ends of the earth.
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Romans 1:16
For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek.
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Matthew 13 v.18 Hear then the parable of the sower: 19 When anyone hears the word of the kingdom and does not understand it, the evil one comes and snatches away what has been sown in his heart. This is what was sown along the path. 20 As for what was sown on rocky ground, this is the one who hears the word and immediately receives it with joy, 21 yet he has no root in himself, but endures for a while, and when tribulation or persecution arises on account of the word, immediately he falls away. [2] 22 As for what was sown among thorns, this is the one who hears the word, but the cares of the world and the deceitfulness of riches choke the word, and it proves unfruitful. 23 As for what was sown on good soil, this is the one who hears the word and understands it. He indeed bears fruit and yields, in one case a hundredfold, in another sixty, and in another thirty.