I have just been wondering about this. I get that we can derive the meaning of the words based on the context but how do we know that a particular symbol is pronounced in a particular way?
I thought about this because I was looking at how there is a clear similarity between modern Chinese writing and ancient Chinese writing, yet I have no idea how they pronounced the words despite understanding what they are saying.
I don't recall anyone asking about Assyrian pronunciation before, so hopefully one of the historians of the ancient world or linguistics can help you out with specifics, but the general question of 'how we know' how an ancient language was pronounced is a common one here. You may get something out of these earlier threads; the first group are more on-topic, but you may find additional specifics sprinkled throughout in the second group
How do we know?
How were specific languages pronounced
What did the language spoken by the Ancient Egyptians sound like?
What did Megas Alexandros and Julius Caesar actually sound like?
Do we have any clue how Latin was pronounced and how it sounded like in ancient Rome?
Original pronunciation of "Ceasar"? <-- in particular this comment
How do we know "YHWH" in the Old Testament was pronounced as "Yahweh" and not anything else?
What is the furthest year I can go back in time to England and be able to communicate with people?
Not to discourage discussion, but if you don't get an answer here you may want to try asking in /r/linguistics or /r/asklinguistics.
Well for one, the Assyrian language is still alive. https://en.m.wikipedia.org/wiki/Assyrian_Neo-Aramaic