How would anyone ( but God and Christians in heaven) know he got saved if he lived and died by himself all alone?
People in doubt have always created this hypothetical scenario: " What about those who never heard of Christ" or " What about the starving African infant who dies" and on and on it goes, creating all sorts of situations, trying to create another gate/ doorway into heaven - When Jesus clearly said, I AM THE WAY, THE TRUTH AND THE LIFE, NO ONE COMES TO THE FATHER BUT BY ME.
People cannot accept that Jesus is the only way. And so people like you say, " I get it, I understand what the Bible claims ... but what about this ... or that ... dig deeper". You are searching for another way into heaven, an excuse.
We cannot concern ourselves with those who already passed on. God judges people based on truth ( reality) that has been given them, revealed to ALL of them.
Romans 1 says man is without excuse .
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness, because what may be known of God is manifest in them, for God has shown it to them. For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse, Romans 1:18-20
So, this scripture states no matter a person's knowledge of Christ or not, the TRUTH has been manifest in them, God shows it to them. Jesus is the TRUTH.
That is the inward, spiritual calling of God to all. His attributes are clearly seen and experienced - even by that guy on your hypothetical island. Technically, according to this passage, no one is left out, deprived from the opportunity of realizing and having a relationship with God - no one has an excuse!