while growing up in canada means you've been raised in the west and are a westerner regardless of what you look like, it's important to point out that the west is not the only culture that was dominantly influenced by the greeks. it was perhaps a pitstop in the long run of things, but greek mathematics and astronomy, especially, were developed rather substantially in baghdad during the babylonian renaissance; the centrality of greek origins in this renaissance is itself rooted in the deep cultural realities of centuries of hellenic dominance in the region, from the persian collapse led by alexander through the parthian uprising and well into the roman takeover of the levant, led by pompey. the roman-persian war was initially built on a struggle as to who would inherit the greco-persian empire, a question that history never resolved, until the appearance of islam, which did not inherit it but dismantled it.

that ancient hellenic influence, as projected by alexander (but, in fact, preceding him, culturally) spread to the furthest eastern reaches of the indo-european sphere, and all the way into india itself. the legend is that very large numbers of alexander's soldiers ended up india when he died and just kind of stayed put there. when they did, they set up colonies with their own systems of government and manufactured their own art and whatnot. cultural exchange between these greek settlers, called indo-greeks and greco-bactrians, and the indians themselves was in fact exceedingly deep, and the effects of hellenism in india can be traced very far into the future.

i mean, check this out:
https://en.wikipedia.org/wiki/Hellenistic_influence_on_Indian_art

it's a deep academic discipline - well studied, because it's so prominent in the art.

while i'm not aware of any tradition of plato or socrates in india, the period of hellenic influence in india coincided with the earliest buddhist writings, and it's hard not to see an influence from greek discourse on the way that the writings are ordered. it's known that many extant buddhist sculptures were essentially greek in construction, so the influence was there. regardless, buddhism is also a discourse-based system of thinking, rather than an authoritarian one.