This is a basically question about sources. I’m curious whether the information we have today about ancient civilizations is largely what we can expect to ever know about them, or if there is any sense that we may discover more in the future, possibly because of technological advancements?
Undoubtedly, yes. We learn more about the ancient past every day.
The assumption that we're not likely to find anything new comes from the fact that our main and most traditional introduction to the ancient world is literary texts. Classical literature is a fairly fixed body of evidence. While new texts are occasionally found on preserved papyrus (including the charred scrolls from Herculaneum that new technology has made partially legible), it is not very likely that we will ever fill the enormous gaps in the literary record. But this is only one type of evidence, and its relative stability is not typical.
The big gains we are constantly making in our knowledge come from archaeology. Countless ancient sites remain only partially excavated or not excavated at all; huge stretches of land in the core areas of ancient civilizations still await study through survey archaeology. Every new excavation turns up vast quantities of evidence - not just in the form of the buildings and spaces uncovered, but in material culture, art, inscriptions, coins, and human and animal remains, and the patterns of their distribution and interconnection.
All of these things can serve as multiple kinds of evidence for ancient history. For example, pottery can tell us about daily life, but also trade networks, and often comes with decoration that provides information about leisure-class culture, daily life, dress, military equipment, and so on. Coinage similarly tells us about the presence and distribution of wealth but also has iconography that can help with dating and tell us about ideologies and self-image. Inscriptions on stone, metal and pottery contains a wealth of information about political culture, civic ideology, burial and commemoration, public spectacles, religion, trade, food, warfare, and any other theme you can think of. Whole subdisciplines (numismatics, epigraphy) are devoted to such forms of evidence. Every single object also tells a story by where and in what state it was found, what other objects were found around it, etc.
Though new technologies are sometimes applied to the study of ancient history - for example, satellite mapping, or using laser surface scanning to reconstruct text on stone - most of our growing knowledge does not require any new technology. All it requires is the continued diligent effort of scholars all over the world, and the continued investment of local authorities in excavation and preservation. Indeed, with many large bodies of evidence (such as the British Museum's collection of cuneiform tablets) the great limiting factor on the development of our knowledge is not the quantity of sources, but the scarcity of resources (skilled labour) allocated to decoding them. Due to the precarious position of archaeology, ancient history, classics, and other forms of ancient world study in the neoliberal political economy, we quite literally have more evidence than we can handle.
I should add, though, that this wealth of material isn't likely to shake our general understanding of ancient history to its core. The reason for that is partly inertia (there is always resistance against changing paradigms) but also partly the fact that the bodies of evidence that are growing - mostly material - do not tell neat stories in the same way as the body of evidence that is hardly growing. A book that outright tells you "I am going to tell the story of how Rome conquered the world" (Polybios) is always going to be more evocative and persuasive than a handful of coins and some postholes. It takes a great deal of work, skill and imagination to distill a narrative out of the vastness of archaeological evidence. But it is happening - especially for those areas that have never been well served by the limited interests of the literary sources.