If the large empires of the Assyrians, Chaldeans, and Persians dominated the entire Near East for centuries, why did the small state of the Israelites have a great impact on Western civilization?

The small state of the Israelites had a great impact on Western civilization due to their religion.

Explanation:

Remnants of old tools, whether they be crude stone or remaining biological matter.  The biological matter can be carbon dated, and many of the items have ended up in strata that also define their dates.

As to other information, fire construction, cave paintings, and other artifacts can illuminate many items about an early agrarian civilization.

Finally, the selective breeding of a plant can determine many what's and why's of a society.  Just as one example, the orange was originally a fruit mentioned in Chinese writings before BC became AD.  It is a bred species.