A good question. To answer this question we need to understand how God judges and how God saves people in Jesus then I will address the South American people question.
How God Judges
God will judge everyone as you already know. He will judge everyone on the basis of their works. The book of Romans chapter 1 verse 18 -23 explains how God has made it obvious to everyone since the beginning of time that he exists, and his authority (power) and goodness (divine nature) has always been plainly known.
The problem is we turned this plain knowledge about God into something else, we worship animal Gods (as the African’s do) or as westerners tend to do worship wealth and ourselves over God. We also go against God’s goodness and live selfish lives. Because of this God will judge everyone as guilty. For no one has ever lived their life without rejecting God, except Jesus, Romans 3:10-12.
In the end all people are judged to be going to hell because we all have rejected God. So the question is not how can South American’s be saved but rather how can anyone? We all deserve the judgement of guilty.
How then is anyone saved?
As you alluded to it is Jesus that saves us. Jesus’ death on the cross paid for the sins (our deliberate ignorance of God and the wrong things we do) of all that choose to follow him. Jesus experiences God’s judgement instead of us and was declared as guilty when he died on the cross. But as Jesus had never sinned he could not remain dead and now lives with God in heaven in a real body like yours and mine except it will never die. This means for Christian that God accepts them only because that have placed their trust in Jesus as their saviour (Jesus death on the cross) and their master (Lord).
This is an act of mercy by God, for it is he that makes people follow Jesus through the work of what the Bible calls his Holy Spirit. Without God’s intervention no one would be saved. Mercy is very different to justice. Instead of being condemned Christians are saved as an act of grace or as a undeserved gift.
So what about those South Americans?
In the end the South Americans who have not heard about Jesus are judged fairly because they are judged according to what they could have known about God just by observing the world. This knowledge is limited but it is enough for people to make a choice about God. Such people are judged by what they did with what they knew. (This also helps us to understand God’s attitude towards children who die)
We need to remember it is God who saves. Early missionaries to Africa discovered that even though no one had told some African tribes about Jesus, when they arrived they accepted Jesus readily because God had prepared them. God does not need human involvement to make someone a Christian he is powerful enough to do it by himself. Instead God likes for his people (Christians) to share in the work he is doing as well which is the norm, the miraculous conversion of some African’s was the exception.