This is an interesting question and will drive us in a few directions at once. To give some form to the response, I'll tell you now that we do have good reason to believe that there exists a strong relationship between, say, the Oxford text of Julius Caesar and what Caesar wrote. Yet this last thing, the original text of Caesar, would have gone through adventures of its own on its way to the modern world, as you correctly observe.

Let's step aside and imagine a likely scenario. If it were the case that we knew of Writer X from just a single manuscript, then we would have a real problem. In this case, we would find ourselves reliant on external and circumstantial aspects of the work: we might note that Writer Z, whose works exist and have many manuscripts found in different places, refers to Writer X in their own writings. We would then be able to make the reasonable supposition that we have a text that relates to that known to Writer Z. We might also consider the style of the work in a number of ways to see if it is credible. The Latin and Greek languages can, in some cases and with a degree of confidence, be studied on the basis of style in such a way that you might then deduce that your Writer X is plausibly a Greek of the First Century BCE as he claims to be. Perhaps this would just mean the observation that, like a Diodorus, he somehow exemplifies a developed koine style. Or, to imagine further, let's say that we have just one manuscript of one work of Writer X, but we have twenty manuscripts of another. We could then study the more attested work quite closely, contemplating what might seem to be marginal things: the rhythm, how the author likes to construct periodic sentences, word choice, "style". From studying work 2 of Author X in this manner, we could then return to work 1, the less attested one, and then make a judgment, on the basis of these linguistic features, of whether we read the same hand.

Now, you might still wonder, and reasonably so, why the nature of "work 2", with its twenty known manuscripts, gives us so much reassurance. If you look at the preface of a scholarly Greek or Latin text, you will usually find charts explaining the lineage of all of the attested manuscripts, these explaining the "biological" relationship between them. This is established by close analysis of where the manuscripts do and do not differ. From this kind of process we might notice that, of our twenty, manuscripts 1-15 all have the word vocatis in an ablative absolute grammatical construction in "that passage in chapter 23", while manuscripts 16-20 have the slightly different word evocatis. From this we deduce that manuscripts 1-15 are nearer to one another in the lineage of the text; that is, if we imagine a historical progression from the hypothetical moment of authorship in the ancient world on to the present, we have now identified an intermediate point in the development of the text where two separate manuscript families existed. These might (and probably would) exist on the basis of historical movements in their own right: say, (for the sake of imagination) manuscripts 16-20 represent an earlier level of the tradition, and, let's say in precisely 1342 CE, a monk visited the facility responsible for 16-20 and made a copy - but he makes a mistake, he drops the e in a moment of carelessness and passes along the reading vocatis rather than evocatis. His mistake becomes the grandfather of the written tradition that produces manuscripts 1-15. More complicated versions of this sort of reasoning, what is called textual criticism, allow scholars to create hypotheses about the development and change of texts as they moved through hands from antiquity to the present. They also allow scholars to make meaningful guesses about the original state of the text. In my hypothetical scenario, we would have reason to think that Writer X was more likely to have written evocatis than vocatis.

As for original material that is not known through tradition and detective work, there is not a lot. For that you would have to look to areas often falling outside the bounds of literature, though very interesting in their own right. Greek and Latin epigraphy provide us with massive quantities of original and often datable materials. It would be impossible and improper for me to try to explain in this post how important they are for asking historical questions about the Ancient Mediterranean. That said, I should mention that inscriptions generally provide a very particular type of evidence: lots of tomb stones, lots of generic legal and economic pronouncements, sometimes lovely poetry. We also have papyrus, which does from time to time give us original pieces of literature from antiquity, but this is often in a highly fragmented state and is for the most part Greek, not Latin.

I hope that this was somewhat interesting and would be pleased to make clarifications!

Bibliography

Wilson, N. G. Scribes and Scholars: A Guide to the Transmission of Greek and Latin Literature (Oxford, 1968) [Wilson is still a sort of go to for this question in intro grad work]

Woodman, A. J. Velleius Paterculus: The Augustan and Tiberian Narratives (Cambridge, 2004) [Velleius is a good example of an author with a highly fraught textual tradition that has required substantial intervention (and restraint) from scholars. Woodman's introduction to the problem is exemplary for the issues we're dealing with.]