Short answer: That depends a lot.

I am an achaeologist, but I am based in Europe, so my knowledge of American archaeology is limited. But we do have archaeological sites here for which no written sources exist, so I will try to provide some information in general.

Archaeology as a science you can imagine like a real big jigsaw. But, because it is a very old and much used jigsaw, a lot of the parts is now lost. Moreover, you don't have the package any more so you don't know how the picture as a whole was supposed to look like. So you look at the pieces you have accumulated and try to find out which pieces fit together and where their position in the overall picture is supposed to be. When you think you found out everything you can about your pieces, you put them in a nice little box, describe as meticulously as possible how they look, what you think of them and why and put them on the table for everyone else to see. And maybe later on, other archaeologists find new pieces that match yours and reveal a bigger part of your picture.

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So far for the analogy. The key to every archaeological excavation is documentation. This does not only mean the finds, but especially the traces we gather from the soil. For my region, written sources start with the Romans. Before that, we have different cultures settling in my area for a certain time, and yet older groups of Humans with a hunter/gatherer tradition who kept constantly moving. They used stone artefacts. For this people, we can provide information either when they periodically took shelter in caves or there are finds from places where they processed the raw material to tools.

When people started agriculture, there are farmsteads. These leave traces in the soil, because there are buildings to live in, fire pits, latrines, wells and so on. Every activity that requires digging a hole in the ground leads to the refilling of that hole later on with different material. A skilled archaeologist who knows his area can see and interpret these traces. And when humans live there, usually there also is waste. Parts of this waste often don't survive til today, for example organic materials rot, but others do: Coins, broken pottery, stone tools are quite durable. So, everything we find is fotographed, drawn, described and catalogued.

Supposing you don't know anything about the things you found, the next step is looking for similarities. You can look out which other archaeologist found similar pottery in another spot. Or similar layouts of houses. You notice the similarities and the differences. But likely people with the same set of tools and ceramics in the same region lived at the same time, even if you do not have a clue when exactly that was. Back to the analogy, you found pieces on the table that don't exactly match yours, but are likely to be in the same area of the jigsaw)

So, let's imagine that people lived not only once for a few generations, but chose the same spot on different occasions. So, during excavations, you find traces of human accoupation lying under the horizon you were working with. As layers tend to accumulate on top of each other normally the things higher up are younger, and the archaeology deeper down is older.

So you can establish a relative chronology, even if it may be you still have no clues when each phase of that settlement exactly was occupied in and if they followed directly or if there was a hiatus.

Next step would be to try and find out if all the things you found could be produced locally, or if there was some sort of trade involved, which would mean you could try to compare your finds with another region where eventually the timeframe might be clearer. At least, you can find hints of a more broader picture and how your settlement connects with the world outside. But you have to look what other archaeologists brought to light.

So now, I want to come back to your question on specific events without written sources. In my broader area, there is a kind of crime scene investigation taking place, because during an excavation, there has a mass grave at Herxheim been unearthed that dates back to the Neolithic and was inhabited between 5300 BC and 5000 BC. During the later phases of that settlement, a lot of sacrificing Humans seems to have occurred, and a lot of bone material has been unearthed. The bones were marred and cutting traces on them, which anthropologists interpreted and dated. (Andrea Zeeb-Lanz (ed.): Ritualised Destruction in the Early Neolithic – The Exceptional Site of Herxheim (Palatinate, Germany) (= Forschungen zur Pfälzischen Archäologie Band 8.2), Speyer, 2019, ISBN 978-3-936113-15-0.)

Thanks to the technical progress, a lot of scientific wizardry is now accessible providing better dates in several methods, that make it easier to accomplish a broader picture of such sites. But without written sources it still is noticably harder to get an really exact date. But, as I was trying to tell you when I began writing, we collect data also for future scientists to work on with what we provided.