Short answer: We don't. There is no 100% confidence that an ancient manuscript surviving only in later copies really was exactly what it purports to be. We do not even often know for medieval works what the original work looked like precisely--few autograph manuscripts survive. Historians and others who study these earlier periods have to make peace with this uncertainty, and an analysis of sources and their reliability and authenticity is usually a significant part of any decent historical monograph regarding the ancient and early medieval world. But there are ways to raise that certainty well above zero.

That being said....longer answer.

There are a number of techniques manuscript historians and others who study the transmission of texts can use to raise the level of certainty about a particular work's authenticity as an earlier work, even if the only surviving copies are much later than the purported date of the text. It's interesting you mention Hellenistic texts--something that should be mentioned about Greek texts is that for some, we actually have considerably older manuscripts than for others. Herodotus (who is pre-Hellenistic) is an excellent example -- we have parts of his works on papyrus manuscripts dating back as early as the 1st century AD, as well as medieval copies. Compare that to the historian Polybius, where the earliest extant manuscript dates to the 10th century and is a palimpsest, which means it was written on vellum that was subsequently reused for another purpose. The earliest full manuscript is only the first five of 40 books, and dates to the 11th century. But we also know the Byzantine emperor Constantine Porphyrogenitus had excerpts from Polybius compiled into what's known as an epitome, which also survive--it's what helps us know that there were originally 40 books. Then, there's an author like Thuycidides (also pre-Hellenistic), where the earliest manuscript dates to the 11th century.

By comparing the texts of various manuscripts that are known, we're able to determine how they were related to each other, building what's known as a stemma -- a sort of manuscript family tree. That helps us understand what is most likely to have been the original text. In many cases, we also have the histories of the text themselves--where and how the copy was made--which can give us clues to what the original text must have been. In some cases, we have to depend on a single manuscript for what we do know. We also can look for quotations of the work in other works and attempt to fit these quotations into the "puzzle." And we can look at the text itself--its language (whether in Latin, Greek, or a translation of the latter into the former) and how that language itself is used--is it in keeping with what we know about the written language of a particular period in time, as well as looking at the events described and whether they fit in with what's known from other writers and even archaeological evidence. This is what can help sort out a legitimate text from a forgery. (That being said, true forgeries are rare; what's more common is that an anonymous text is attributed to a more famous author, which doesn't necessarily rule it out as a useful source--it just means more work is required.)

For understanding whether a work in a larger sense is truly ancient, one of the better indicators is whether successive writers use it, know it, or quote from it. Thuycidides, for instance, is first mentioned by Theophrastrus about 100 years after he wrote (along with Herodotus), and he's a huge influence on 1st century BC orator Cicero. Polybius, in contrast, was cited by 1st century BC author Dionysius of Halicarnassus as being a writer "that no one endures to read until the end." (Both he and Polybius, incidentally, end up in that Byzantine epitome made by Constantine Porphyrogenitus--which ends up being a valuable source for his works as well) Polybius, however, had friends in high places, including Pliny the Elder and Scipio Africanus the Younger, and being boring is definitely better than being forgotten altogether.

So: Using these examples, we have solid evidence that Thuycidides, Herodotus, and Polybius write particular works at particular times. We don't always have the complete works, and we often have to rely on much later manuscripts to relay what texts we do have. So while we can be nearly 100% confident that there were writers by these names, we will never be 100% sure that the texts that have been transmitted are identical to what these men wrote. But understanding this is part of the overall critical analysis of any historical source.