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You're missing out the interconnectedness of scientific developments that link advances in Africa (writing and numbers) to the Middle East (mathematics and medicine) right up to the expulsion of scholars from Constantinople into Italy that fostered the Renaissance. European Colonialism (and science) was simply the latest stage in scientific development and progress.
Granted, the Arab World, India, and the Far East probably could have advanced on their own, if they'd had the right factors to work with.
Unfortunately, however, they didn't. Their cultures were also too mired in anti-progressive world views to even think to try.
The West changed their thinking in this regard by tearing down the existing status quo.
SubSaharan Africa and South America, however, were a bit farther behind than even that. They were basically stuck at Bronze and Iron Age levels of technology and development, with little hope of moving beyond those limitations at any point in the foreseeable future.