Clearly there is such a thing as an archaeological fact. And sometimes that is what "hecho arqueológico" means. However, I don't think that's the case here.

Obviously, in general terms, "hecho" sometimes does and sometimes doesn't mean "fact". To quote the DLE definitions (which are not as helpful as they might be), hecho (noun) can mean:

"4. m. Acción u obra.
5. m. Cosa que sucede.
6. m. Asunto o materia de que se trata."
http://dle.rae.es/?id=K4rxA9a

Thus "hechos" can be facts (atenerse a los hechos), but they can also be deeds or acts (Los Hechos de los Apóstoles) or events (hechos que cambiaron la historia).

And sometimes none of these translations is right. What about "Introducción al Hecho Religioso", an academic subject in Spain? It's not religious fact or deed or event. It really means religion itself, and that's how I would normally translate it:
https://www.proz.com/kudoz/spanish-to-english/religion/14359...
https://www.proz.com/kudoz/spanish-to-english/education-peda...

But if you had to choose a word for "hecho" in "hecho religioso", I think it would be "phenomenon". It means the phenomenon of religion, and one of the answers to the first of the questions just cited used that word.

"Fact", in English, almost invariably means truth, or expresses truth value. Fact is opposed to fiction or falsehood, or to theory, or to speculation. An archaeological fact is not a physical thing, it is an abstract truth supported by evidence. And in Spanish it is called an "hecho arqueológico".

The impeccable source Adriana has cited refers to archaeological facts:

"This is why the archaeologist’s field notes and his published report become primary archaeological documents. They are not themselves, strictly speaking, archaeological facts: they are the excavator’s interpretation of what he saw, or thought he saw, but this is the nearest the discipline can ever get to archaeological facts as established by excavation."
https://www.britannica.com/science/archaeology

Archaeological facts here are truths of an archaeological nature, truths about the past supported by archaeological evidence. When it says that "this is the nearest the discipline can ever get to archaeological facts as established by excavation", it means the objective truth about the past.

But in your text it seems to me that "los conceptos generadores y fundadores del hecho arqueológico" is not referring to the concepts that generate archaeological fact. "Hecho" here is being used in a sense similar to "hecho religioso". It means an archaeological phenomenon, something that archaeologists investigate and that requires consideration of all sorts of evidence.

It is notable that "archaeological fact" is not an expression you tend to find English-speaking archaeologists using in this sense when discussing of the modern epistemology of archaeology. When they do use it they simply mean archaeological truths supported by evidence. But they do use "archaeological phenomena" to express the broader, post-positivist conception of archaeology that I think "hecho arqueológico" refers to:

"Very much more difficult issues arise when we seek to understand the ways in which time (and the playing-out of complex formation processes over time) can structure archaeological phenomena—literally the things archaeologists observe and seek to understand and explain.
[...]
If one takes a different view, however, about the distinctiveness of archaeological epistemology [...] then a consideration of a distinctive archaeological ontology is more than justified—if only to emphasize that such theories may well require substantial transformation in order to capture the different essences of archaeological phenomena."
https://books.google.es/books?id=xq4rNwV0w44C&pg=PA170&lpg=P... (pp. 170, 177).