[citation needed] Far more evidence for it being a European phenomenon derived from Hellenistic philosophical traditions like that of Plato and Aristotle, especially because whenever those two were taken as a major influence, like during the Islamic Golden Age, science and learning suddenly starts advancing really quickly.
Where Christianity factors in is science being a Christian project
This is a
huge subject with a ton of branches to start tackling. It can never really be pinned down to a
single factor, not entirely, but we have our preferences. Your mention of Aristotle reminded me of the time the Chinese circulated the idea that he was
never real.

The Chinese had a school of thought called
Mohism that appeared around the same time as Confucianism and Daoism that was in many ways similar to the ideas of Aristotle (including a school of logic that could have had them on a similar, European trajectory). It only survives in fragments because when the Qin dynasty took over, they destroyed anything that wasn't abject totalitarianism (
Legalism), hierarchy and authority worship (
Confucianism), and relatively worthless mysticism (
Daoism). Through most of their history, the Chinese have made great things, but destroyed them when the new dynasty takes over, and was so preoccupied with remaining stable that the status quo was prime and true innovation and new fields of philosophy were basically quashed in order to maintain social stability. China normalised destroying parts of its past to maintain the present, and effectively slowed their progress into the future. Whilst this generally represents why China experienced slower technological progress and social reform compared to the West, it also provides an important factor (one amongst many it can't be overstated) to compare between different parts of the world.
In Europe and the Middle East, despite the occasional bouts of iconoclasm and whatnot, texts and works were still preserved in some capacity and a great deal of time was spent considering and pouring over them. Despite the presence of orthodoxy and what you've heard of burnt heretics and the like, logic and reason were still integral to both philosophy
and theology and would remain so for centuries.
Natural theology essentially categorises the co-existence of faith and logic seen in people like Aristotle and St Thomas Aquinas, who both tried to use the latter (logic) to assert justification for the former (faith) – though not universal some Greek philosophers did veer into the concept of a
divine being greater than the rest, so it probably explains why their musings were so easily transferred over to Christian thinkers.
Though NT is shunned today by the religious in favour of
Fideism (In the context of how NT influenced
George Lematre and
Darwin? Pretty understandable), the Catholic Church still considered the logical existence of God rather important. They were included in the
Summa Theologica in the form of Aquinas'
Five Ways. And in those instances where they just burnt people? The person had to argue their perspective and the ones carrying out the punishment had to counter-argue why they were wrong.
Fides quaerens intellectum; faith seeking understanding. First believe, then understand – this was the relationship between faith and logic for the time period pre-Renaissance.
And this is just me touching on the theological/religious side of things of one part in one aspect of European history.
"Standing on the shoulder's of giants," is pretty emblematic to me of how Europe managed to surpass other parts of the world. It encompasses a lot of different things so it's admittedly a copout, but I think it generally wraps up why Europeans leapt over everyone else with a nice neat bow. To facilitate it you'd need a bare minimum a writing system to preserve ideas whilst not being inhibited by some cultural/philosophical practice. If you wanted to attribute it specifically to Christianity, the major component is the fact it's monotheist which is where the Greeks tended to end up, though theirs was more akin to
monolatry (multiple gods, but one supreme god). Considering the machinations of a single deity whilst also trying to prove he exists is far less mentally taxing and makes it viable for exploration. If you
really wanted to, you could put it on the fact the Europe's faiths had a definitive, physical reality that was created through direct action rather than being a "manifestation" or created instantly. One trend I've noticed – and I haven't seen
every religion's creation story so no definitive statements – is that European faiths have the world created or formed in a sequence (individual gods creating individual components, or the single capital-G God making it over the course of days) whereas in Hinduism, the Earth was already formed whole it just had to be split from the sky and heavens. Since we can see the world is made of hand-crafted (relatively speaking) components, then we can consider those components, which helps the development of existentialism – like Plato's
Theory of Forms.
Oral tradition was a thing in some places (North America, India, Steppe Nomads, etcetera), but you could probably come up with reasons on the spot why that's not as good as written word. A basic combo of "no writing system" + "no tradition of logic/introspection" are two major ones that explain why a lot of the world remained behind. Whilst you could consider biological and inherent aspects that had some part to play, "no written language" is easier to point out the direct cause/effect of. Contrived example of how biology could (possibly) factor into development/unfiltered-schizophrenia:
East Asians largely have no body odour, and have less tolerance for lactose. The latter contributed to the raising of less cattle in favour of pigs, and the former lead to less impetus for potent soaps like in Europe. Pig fat isn't as good for soap-making as beef tallow, hence why Chinese soap was primarily plant-based and wouldn't make use of animal fat until into the modern era. European soaps, primarily made from animal fat, produces the by-product of Glycerol, which when mixed with nitric and sulphuric acid, produces Nitroglycerin. Nitroglycerin leads to dynamite and both of these products were invaluable in the development of infrastructure and resource gathering which contributed to the second industrial revolution.
TLDR: Many East Asians don't have body odour -> no soap priority -> no familiarity with its components (glycerine) -> no explosives (nitro-glycerine).
India: No written history pre-Islamic/Persian conquests in the North. We only know vague what happened here due to the Chinese or neighbouring Persians picking up things here and there. Alexander the Great's brief foray into the sub-continent did more to preserve Indian history than the Indians until they began to bother with keeping records.
Meso-America: They had
Quipu in the region, but that was only good for numerical records. The Mayans had a script of sorts, the sort that usually preceded development into more sophisticated forms (
Chinese characters evolved from religious inscriptions; it's likely we would've seen the same development with the
Norse/"Vikings" with their runes before they took on the Latin alphabet) and the Aztecs had something
similar.
Sub-Saharan Africa: Whilst it'd be easy just to write them off using the same reasoning as India basically – no writing system, they actually might show what would have happened had the Indians did develop one. It wasn't just a writing system that held back the Chinese, it was their modes of thought, and one of those modes (Daoism) didn't contribute to positively to their development as far as I can tell.
Ethiopia did have a script, but their domestic situation was pretty much fucked thanks to the rapid spread of Islam, and the prevalence of mysticism meant that one couldn't
look for knowledge, you had to be granted it through prayer, contemplation, and surrender of the self. The other civilisation of note, Mali, didn't write its histories down either and we only have Arabs and Portuguese sources for info.
Everywhere else: Same trend. No writing system, heavily reliance on oral histories (Australian aboriginals, Native Americans, etcetera); no tradition of introspection or existentialism.
I don't know how to "TLDR" this other than: You're both right. Christianity had its own part to play but the influence of Greek philosophy is undeniable. I'd only contribute that both those aspects were reliant on the fact we actually wrote shit like that down and spend time pondering it. Greek philosophies and the logic they utilised got re-introduced into Europe around the turn of the millennium and it meshed well with Christianity, but why the Christians weren't as eager to destroy the past like the Chinese were is also a factor in of itself because if they were all simply destroyed then there'd be nothing to help mesh logic with faith, and then logic and all its benefits and flaws wouldn't have influenced the European trajectory.
And that's still just
one part of it all.