This scenario is almost an exact representation of a real life case presented by Evangelist Bill Rice (founder of the Bill Rice Ranch), recounted in his book Cowboy Boots in Darkest Africa. To make a long story short, Rice visited a pygmy village which had never heard the Gospel or even seen a white man. An old man stood up and said, "I thought it must be like that. As a young man I climbed a tree, looked up in the sky and thought, 'There must be a true God.'"
Here's the relevant truth: if anyone seeks the true God and His Son Jesus Christ, they will find Him. God will send someone or provide some way for him or her to hear the Gospel and be saved. They won't need to have some extra-Biblical way of salvation.
"Seek and ye shall find" (Matt. 7:7).
I like this John, especially how you quoted Matthew 7:7. I have always had a similar view, if a man cries out in his heart to know God, God hears and will reach that man.
That said, what a man was required to know and believe has changed in time as more and more was revealed. Adam and Eve only had to believe in the "woman's seed" that would come. I believe that she mistakenly believed Cain was this promised seed;
Gen 4:1 And Adam knew Eve his wife; and she conceived, and bare Cain,
and said, I have gotten a man from the LORD.
Job simply knew his redeemer lives, and that he would see him with his own eyes some day.
Job 19:25 For I know that my redeemer liveth, and that he shall stand at the latter day upon the earth:
26 And though after my skin worms destroy this body, yet in my flesh shall I see God:
27 Whom I shall see for myself, and mine eyes shall behold, and not another; though my reins be consumed within me.
It is fairly safe to assume that Job taught his neighbor and fellow man, and they gained some important knowledge here. God would send a redeemer. What does that mean? It means God would purchase man back who was "sold under sin" as Paul said in Rom 7:14. Job knew God would stand on the earth with men. Job knew his body would be resurrected. So here was new revelation.
The scriptures tell us all men were dispersed at the tower of Babel. These were the near descendants of Noah, so certainly they had some knowledge of the true God. As they went out into all parts of the world, in time that true knowledge was lost or perverted, but all men had some knowledge of the truth. And I believe God's word teaches that he holds them accountable according to how much they know and understand.
Luk 12:47 And that servant, which knew his lord's will, and prepared not himself, neither did according to his will, shall be beaten with many stripes.
48 But he that knew not, and did commit things worthy of stripes, shall be beaten with few stripes. For unto whomsoever much is given, of him shall be much required: and to whom men have committed much, of him they will ask the more.
Jesus said the servant that did not know his lord's will, yet did commit things worthy of stripes shall be beaten with few stripes. I would not like to speculate exactly what this means, only that God will be more lenient with those who have no knowledge of the truth.
We also see from scripture that God "winked" at man's ignorance in the past, but now commands all men everywhere to repent.
Acts 17:23 For as I passed by, and beheld your devotions, I found an altar with this inscription, TO THE UNKNOWN GOD.
Whom therefore ye ignorantly worship, him declare I unto you.
Paul says something amazing here, he said the Greeks ignorantly worshiped the true God.
Acts 17:30 And the times of this ignorance God winked at; but now commandeth all men every where to repent:
Paul implies God was lenient with those who did not know the true God and the gospel. But once a man hears he is commanded to repent.
So, this is a very difficult subject no one has ever answered well, but we can know that God is just, and he will judge all men in perfect justice.