Between the Exodus-era and the Roman era, the Hebrews interacted with many civilizations around them. Is there any record of how those other civilizations reacted to the Hebrew idea of monotheism? Did the Egyptians, Greeks and Romans, for example, deny the existence of the Hebrew god, or did they simply regard it as a foreign god that was not part of their pantheon? (Or did religions such as the Romans try to incorporate the Hebrew god into their own pantheon, much as they incorporated Persian and Egyptian gods such as Isis and Mithras)?
I am aware that the Roman general Pompey (and presumably the Macedonians under Alexander) were confused to find the Jewish temple at Jerusalem to be empty, bereft of statues and representations of their god.
I'm afraid I can only answer for the Romans. In the Roman Empire, Jews were allowed to sacrifice to their God for the Emperor, rather than to the Emperor himself. Other religious minorities had to do the latter. However, following the Great Revolt of 66-70AD, Jews had even this right stripped from them.^1 As for what classical authors thought of monotheism, here's a quote from Tacitus, full of ancient anti-semitism:
This worship, however introduced, is upheld by its antiquity; all their other customs, which are at once perverse and disgusting, owe their strength to their very badness... among themselves they are inflexibly honest and ever ready to shew compassion, though they regard the rest of mankind with all the hatred of enemies... Those who come over to their religion have this lesson first instilled into them, to despise all gods, to disown their country, and set at nought parents, children, and brethren. Quite different is their faith about things divine. The Egyptians worship many animals and images of monstrous form; the Jews have purely mental conceptions of Deity, as one in essence. They call those profane who make representations of God in human shape out of perishable materials. They believe that Being to be supreme and eternal, neither capable of representation, nor of decay. They therefore do not allow any images to stand in their cities, much less in their temples. This flattery is not paid to their kings, nor this honor to our Emperors... the Jewish religion is tasteless and mean.^2
For the full account, see here.
I'd be interested also in how the Assyrians thought of Jewish monotheism, and also, as a fellow monotheistic people, the Persian Empire.
^1 Matyszak, P., The Enemies of Rome (2004), pp. 191-212, and Baker, S., Ancient Rome (2006), pp. 242-289, are great introductions to the revolt and its consequences. The latter sketches a great narrative of events.
^2 Histories, 5.