Actually, it's almost guaranteed. OTL, Buddhism had a presence in eastern Mesopotamia,
Really, Buddhism was a thing of significance in eastern Mesopotamia- basically equating to the Basra area? Well Buddha was part of the claimed prophetic heritage of Manichaenism, and that originated in Mesopotamia I believe.
and with the Indo-Greek and Graeco-Bactrians, the faith was spreading westwards. Also, have the Turks and others choose it, and it will have a presence perhaps as far as the Danube.
Keep the Roman Empire from rising,
Keeping the Hellenistic states as players in west Asia and along the east mediterranean shores may well offer an extra opportunity for Buddhism to spread from Indo-Greek and Graeco-Bactrian areas further west, I wonder if even the expansion of Roman rule has to be a showstopper for the possible spread of Buddhism.
Well Ethiopia might be convertable before it goes Christian. Maybe?
I agree with Beedok. I think even though it did not come to be a significant part of the religious mix in the Mediterranean area in OTL, Buddhism's chances are still far better before Christianity and Islam emerge rather than after. After Christianity emerges it takes alot more work ad creativity.
Judaism in the BC is not that much of a bar to Buddhist conversion (except among Jews themselves).
It seems to me that Zoroastrianism, while not monotheistic, was more systematized and durable than the other paganism. Perhaps if somehow the rise or longevity of the Persian Empire could be aborted (without simultaneously butterflying away Gautauma) and if Babylonian-Assyrian polytheism remained dominant in the fertile crescent, the odds of Buddhism coming to dominate Iraq, and from there, other locations, could have risen quite a bit.
Not sure why Babylonian, Egyptian, Greek or Roman polytheism would be any harder to mix with Buddhism than Indian, Chinese or Japanese polytheism.