The books of the New Testament were copied and distributed widely during the lifetime of the apostles.
Any early changes would have been resisted by them.
After their death, there were already copies spread throughout the Roman world.
A side by side comparison between the two main text families (the Majority Text and the modern critical text) shows agreement a full 98% of the time. Of the remaining differences, virtually all yield to vigorous textual criticism.
This means that our New Testament is 99.5% textually pure. By the end of the first century BCE, Rome had taken over the eastern Mediterranean and the Jewish population was spread through many cities of the east.
Yet scholars are confident of reconstructing the originals with some significant degree of accuracy.
In fact, virtually all of our knowledge of ancient history depends on documents like these.
 Among the nearly 3,000 minuscule fragments are 34 complete New Testaments dating from the 9th to the 15th Centuries. Uncial manuscripts provide virtually complete codices (multiple books of the New Testament bound together into one volume) back to the 4th Century, though some are a bit younger.