So, please correct if I have been misled, but we don't have original documentation from Ancient Greece or Rome. For example, the oldest manuscript of Plato's Republic is from the 9th century. That means we had a thousand years or copying from scribe to scribe. How can we be sure the texts weren't changed dramatically? Do we have any verifiable proof that Aristotle is the same now as it was from 300 B.C.? The same could be said of Cicero or Roman writers.
I know that people doubted the accuracy of the Bible for a long time but the Dead Sea scrolls helped to prove some books of the bible remain accurate from copy to copy. I just don't see or hear of anyone doubting our classical texts.
I covered this questions somewhat before, so I'll be brief here. The short answer of it is bu comparing our sources, so you find 2 copies of Plato's Republic which are unlikely to have a common source. So one copy in Greek from 10th century Constantinople vs a medieval Arabic version from Syria. You can also compare to the papyrus fragments of the Coptic version of Plato's Republic found in the Nag Hammadi library, and then compare with all of the quotations of Plato's republic found in other pieces of ancient and medieval literature. using textual analysis in this way not only can we feel confident about the accuracy or many texts but also can speak as to which surviving versions we have might contain the least errors. It's a fascinating subject.
Here's is my previous response to a similar question: https://www.reddit.com/r/AskHistorians/comments/6831u8/how_do_we_know_that_roman_texts_are_authentic/dgw272h/