IOTL Buddhism's western spread was ended through the rise of Islam. Pre-Islamic Afghanistan seems to have been majority Buddhist. Bactria and Margiana, and Central Asia more broadly appear to be areas of religious flux, where Buddhists, Zoroastrians, Manichaeists, and Nestorian Christians were all found in close proximity. There is the general belief that Zoroastrianism was going through a period of decline even before the Arab invasion, with the religion essentially functioning as the court religion of their state - a status quo which likely would not hold if the dynasty was overthrown.
Regardless, let's presume either there is no Islam, or it's strangled in its grave, never substantially getting out of Arabia. How far could Buddhism spread to the west? Is it possible it could become the state religion of Persia? When the Turkic migrations reach into Central Asia a few decades later, might many Turks convert to Buddhism, resulting in the introduction of the religion all the way into Europe?
Regardless, let's presume either there is no Islam, or it's strangled in its grave, never substantially getting out of Arabia. How far could Buddhism spread to the west? Is it possible it could become the state religion of Persia? When the Turkic migrations reach into Central Asia a few decades later, might many Turks convert to Buddhism, resulting in the introduction of the religion all the way into Europe?