Your question almost answers itself, because a presumed historical Zoroaster (who we will for convenience define as the composer of the Gathas) would definitely not have lived in the Near East. Instead linguistic and textual evidence suggests he would have been from Bactria or thereabout, roughly in modern-day Afghanistan. (Among other things, Pashto is thought to be the modern-day language closest to Avestan, and an episode describes Zoroaster interacting with the king of Bactria).

Anyway, any attempt to answer this question will invariably stumble into a big issue: monotheism is a statement of doctrine moreso than a factual description of a religion. Case in point, some conservative Muslims do not view Christianity as truly monotheistic due to the whole Trinity business. If we consider Zoroastrianism as a monotheistic religion in its (I'm simplifying a bit and skipping some historical ambiguities here for brevity) exaltation of Ahura Mazda to the status of supreme being and relegating of other deities to the status of "Daeva" (roughly demons) or "Mainyu" (roughly spirits; the benevolent spenta mainyu are aspects of Ahura Mazda, opposed to angra mainyu, the spirit of destruction) to be a statement of monotheism, should we not also do the same with Hindu traditions like Vaishnavism or Shaivism, exalting Vishnu or Shiva respectively?

I think monotheism is an unhelpful label, generally. It is a doctrinal self-identifier to differentiate oneself from one's perception of other religions. It may not even make sense at all in some intellectual/spiritual traditions and might even be an obstacle in understanding them on their own terms. Many of those from a Judaeo-Christian background enjoy waxing lyrical about the supposedly unique conditions experienced by the Hebrews leading to the exclusive worship of Yahweh, but that is with 2,500 years of hindsight, having seen Christianity and Islam conquer much of the world previously ruled by the "others", the "polytheists". We easily feel like there's something special about it that really sets it apart and demands explanation - it seems like a development, or progress.

But this is a narrow, Abrahamitic-centric way of viewing the world that risks inhibiting our appreciation for other religious-intellectual traditions, such as Buddhism, which has a very different relationship to the divine. These traditions have their own perspectives, frameworks and idiosyncracies, that distinguish them from others. Some may have something we may feel to be comparable to monotheism, but we need to be very careful indeed with the labels we apply.