For literary works, the chances are not very good. This thread talks about it in more detail.

Literary sources are not the only significant sources for ancient history, though (and in some cases, those literary sources might be worthless for reconstructing the history of events, for various reasons such as bias or outright invention of events). One important fact is that there are large periods of time, and large areas of space, where our literary sources are absolutely silent. It might be that the relevant works are lost, that they are completely unreliable or that they simply don't mention the events that we were looking for.

That being said, there are other significant sources that can help us reconstruct the history of events for Ancient times. These are archaeological findings and epigraphical or papyrological sources. Those emerge all the time, we still find hundreds of new inscriptions every year, and the number of archaeological sources found yearly is probably legion. So the question is, how often do we find something significant? It's not always easy to tell at first glance, since priorities in research shift and things that might have been considered insignificant receive attention by later scholars and get researched in detail while they were overlooked earlier.

Many epigraphic sources simply don't tell us much new, they might simply state an isolated name or record that someone set up an Altar - those can still be significant when put in a wider context, analyzing evolutions over time or looking at the social groups and how they portray themselves f.e. - while others do tell us about important events that are not recorded in our literary sources. Even singular artefacts can be that significant, and since our sources are silent about so many areas, what we know of the history of a whole region might hinge on the interpretation of a single inscription. For example, we don't really know when and ow exactly the Romans abandoned the areas east of the Rhine and north of the Danube. All we know is that there was increasing pressure in the 250s, with Germanic invaders penetrating the borders here and there, as far as Italy or France, though the extent of destruction is not easy to determine and the whole chain of events is very murky. What we do know is that Roman local administration still functioned at least in 253, since we have a surviving milestone that mentions the co-emperors Valerianus and Gallienus. Beyond that, no epigraphic sources survive.

Another example is the Imperium Galliarum, a breakaway Empire centered on the western provinces. Again our literary sources don't tell us much, and we would have never known that the province of Raetia was part of this separate Empire if we wouldn't have found an altar in Augsburg that comemorated the victory of the provincial governor under Gallic emperor Postumus against invading germanic people on the way back to their homes. This single find meant that this previously unknown battle on 24/25th April 260 entered the historic record. Thanks to it, we know that Raetia was part of it for a short while. And furthermore, the beginning of the Imperium Galliarum was put back into the year 260 instead of 259 as earlier assumed, since the dedication took place on September 11, 260, and Postumus, the first Gallic Emperor, is mentioned as Consul for (probably) the first time, which means that he wasn't Consul in 259, which in turn means that the Gallic Empire didn't yet exist back then.

This is just a very flashy example, but many of the inscriptions discovered yearly have some impact on our knowledge for certain periods.