Akkadian
omniglot.com
omniglot.com
[1]: https://oi.uchicago.edu/research/publications/assyrian-dicti...
[1]: https://en.wikipedia.org/wiki/Rosetta_Stone
[2]: https://en.wikipedia.org/wiki/Jean-Fran%C3%A7ois_Champollion
For morpheme based languages (i.e., where the letters make sounds, and then the collective sounds hold meaning), pronunciation can be backtrace by looking at the shifts of child languages. For instance, a lot of english T words had shifted from D words (e.g., 'dens' from french/latin for tooth, to english 'tooth'; many words experienced a d->t shift). When you compare this to other child languages who experienced other shifts, you can sort of triangulate back to the original pronunciation based on how the child languages ended up.
It's sort of like genetics, in a way: if you have two children, one with blonde hair and the other with brown hair, you can infer that one parent had to be blonde.
E: One more analogy since it came to me: Imagine you see a few people walking in different directions, and you want to know where they all started from. You can look at where they are, try to group them in to similar types ('cognates', which words do we think came from the same word), and then look at the path they seem to have been walking down. Then, you draw a line back from where they are, through the path they came from, and hope that the lines you draw for all of them intersect at some point, and that point is your source.
E2: Explaining pronunciation through text is hard.
In addition to other comments: sometimes you are lucky, as when someone figured out that Copts speak ancient Egyptian. It was also a semitic language like Arabic.
Of course none of this can be "authoritative" in a substantive sense: not only must Arabic pronunciation have influenced Copt, but you need only look at contemporary time to see how accents etc can vary widely in short geographical distances much less over time. These variations extend to contemporaneous usage of dead languages: I learnt Latin pronunciation in school which apparently is different from usage in the USA, so I can't even make Latin puns with certain people!
So in the end it's just a general idea and a consistent usage so scholars can communicate with each other.
https://en.wikipedia.org/wiki/Egyptian_language#Egyptologica...
xłp̓x̣ʷłtłpłłskʷc̓ https://en.wiktionary.org/wiki/x%C5%82p%CC%93x%CC%A3%CA%B7%C...
The issue with your theory is the numerous counterexamples of languages from the same region which did not (and in fact still do not in plenty of cases) include vowel indicators in their writing systems, but nonetheless spoke and still speak the vowels.
Also, Egyptian is known to have included "determinative" hieroglyphs for cases where the reading would otherwise be ambiguous; the determinative allowed words with the same consonant structure but different vowels to be distinguished from each other (though the determinative itself did not encode a vowel; instead it indicated what type or category of thing the preceding word was, which allowed the reader to choose the correct option).
Plus your example of a vowel-less word is from a language which does have vowels:
It does seems that Nuxalk (Bella Coola) has lots of consonants stringed together. You can listen to some here. http://archive.phonetics.ucla.edu/Language/BLC/blc.html
Edit: I suspect not. Sigh.
Recommended if you're interested in the preservation of forgotten lore. (It's both about that and becoming some.)