As Diagoras has pointed out at length – and as Jeremiah, Paul, John and the author of Hebrews claimed – any God worthy of the name should be able to speak directly to dozens, hundreds, maybe even thousands of followers! Maybe that’s why Jesus said that only a few would be chosen, because God can’t handle communication with millions or billions of followers?
I do believe other cultures have had independent knowledge of God and other historical events in the Bible (such as the global flood).
One book that talks about this is The Discovery of Genesis: How the Truths of Genesis Were Found Hidden in the Chinese Language by C. H. Kang. He goes though many examples of how the early Chinese knew about YHVH and how it’s recorded in the Chinese language.
For example, the character for boat is comprised of “eight”, “people”, and “vessel”. This is descriptive of Noah’s ark where 8 people entered the ark.
And he goes on with many other examples in the book.
Even in modern times, people are having dreams of Jesus without even heard of Jesus before.
For decades, a well-documented phenomenon has been occurring in the Muslim world—men and women who, without knowledge of the gospel, or contact among Christians in their community, have experienced dreams and visions of Jesus Christ. The reports of these supernatural occurrences often come from “closed countries” where there is no preaching of the good news and where converting to Christianity can invoke the death sentence. But these are more than just dreams. Setting them apart is the intense reality of the experience and the surrender of one’s heart and mind to Christ in the wake of the dream. A common denominator appears to be that the dreams come to those who are seeking—as best they can—to know and please God.
So, yes, God has and does speak directly to other cultures and is not “limiited in his communication skills”.
But, getting back to my point, the most objective evidence is written documentation that has been attested to by multiple people.
The Bible is best thought of as an anthology by multiple authors and not just a single (human) author. We have multiple people attesting to what God has done. And not only that, it has gone through a “verification” process in which only the books that has been de facto accepted has made it into the canon. Other religious texts have been written, but have not been considered to be in the top tier. There is also a continuum for this. Some books might not be considered canonical by some, but should be considered canonical by others. For example, I think the Didache should be canonical. And if the book of Revelation was not canonical, I would not get upset.
In the Old Testament and the New Testament, there are certain books which would be considered the core. The Pentateuch and the Gospels I believe would be universally accepted as the core books (esp since practically all Bibles places these in the very front of the OT and NT sections). The other books of the Bible would surround the core. And as we move farther from the core, it becomes more debateable if it should or should not be considered part of the Bible (Deuterocanonical books comes to mind).