Just so you know the early Islamic history in it's first 2 centuries itself are rare. So having a non-Islamic source is far more rare in this situation.

Even the best known early Islamic sources only came after 2 centuries

Tarikh al-Tabari by al-Tabari (d.923 C.E.)

Futuh al-Buldan by Al-Baladhuri(d.892 C.E.)

Kitab Tabaqat Al-Kubra Ibn Sa'd(d.845 C.E.)

Compare to Muhammad's death at 632 C.E. big difference.

A big misconception I will throw out is Muhammad' didn't introduce monotheism, Judaism was big with Himyarite Kings, you got Christians people of the Nestorian faith and you got Arabian polytheism.

I would recommend Events in Arabia in the 6th Century A. D., I never read it but other book I have recommends, it contains information about inscription in certain page.

There are some poems that predate Islam but were preserved for similar reasons to the Christian preservation of classical art.

What I probably should have asked was what non-Islamic sources do we have on Arab paganism/polytheism, particularly in the in Western Arabia or the Hijaz? And to be more specific, what do we know about their rituals? In other parts of Arabia we actually do have a descent amount of historical artifacts to paint some picture, but in the Hijaz it is seemingly nothing. I'm sure Muhammad's/Islamic empire's expeditions which included destroying pagan items played a part, but I would think there must be something left.

This is somewhat of a tangent, but my hope is that it can serve you as pointer.

Years ago I read something along the lines of how the "wise men from the east" who came to visit the baby Jesus in Bethlehem were not coming from Persia, but from either Ethiopia or Yemen, because from these countries the good incense was traded.

Now, if this is true than that would mean that for the contemporaries of the church founders it was a somewhat plausible event to have astrologers from Arabia who deal with incense.

Therefore I suggest to see if you can find something by researching the history of the trade with incense?

What about sources from Ethiopia? Maybe they have to say soemthing about Arabian culture in those days?

Again spice merchants form Arabia are mentioned in the book of Kings, which would predate the church writers by at least a couple of centuries.

"Beside that he had of the merchantmen, and of the traffick of the spice merchants, and of all the kings of Arabia, and of the governors of the country." 1Ki 10:15

I think we can infer a few general points. For example that the people and chiefdoms of Arabia where actually in existence back then.

Incense was and is used for religious purposes. So the Arabs have to have been in contact with various religious customs from different areas. After all that's where the money came from, from their perspective.

These were many words for a minor point. I just hope it was useful.