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"I see this in reverse: the chart of global GDP over centuries"
but that's just a modernist version of the weak anthropic principle
i.e. you only have a chart of rising per capita GDP for the past few centuries because in order to belong to a society that does things like produce charts of per capita GDP, you'd have to see rising per capita GDP in your recent past
progress was quite slow for at least tens of millennia until rather suddenly a number of contingent factors conspired to create the conditions for industrialization, most particularly new attitudes toward human slavery
but it's very easy to misread technological progress for commercial/social progress
why didn't Romans use spinning wheels or windmills or animal labor? because slaves were cheaper
why didn't Romans do more agricultural engineering? because taking Egyptian grain was cheaper
why didn't Romans develop better math? because they had Greek slaves for bookkeeping and little need for complex non-military engineering (again, slaves)
why didn't Romans develop metal movable type? clay was cheaper and if you need lots of copies you just bought more slaves (the printing press in particular seems to belong to a historically very peculiar Protestant notion that everyone should read the sacred texts)
why did Ali Pasha bring all his wealth to battle at Lepanto, while the merchants of Venice financed the casting of some of the most sophisticated weapons yet built with money safely hidden in banks? Europe had sophisticated credit markets, the militarily stronger Ottoman state did not
why did the Queen of England initially ban power looms? she was afraid it would put weavers out of work
everything is deeply contingent
most contingent of all, of course, was the scientific revolution, dependent on a notion of "free inquiry" so unusual to human societies it arose only once and has been under constant attack ever since (despite being inarguably priceless)
progress only looks inevitable in retrospect because once anyone succeeds in raising productivity, others must imitate or fail
I realize this is a made-up scenario, but Westerners tend to assume it's irrational for those in poor countries to maximize their number of offspring. There's a number of factors (labor value tradeoffs, insurance against periods of inability to sustain sufficient income esp at end-of-life) that militate otherwise. Minus could result in a huge amounts of unintended disutility, particularly as populations age.
As pointed out above, the best option is to move the poor into situations where institutions are stronger, producing higher incomes. However, this is very difficult on any large scale. For instance, moving the entire population of Africa to Norway (ignoring space constraints) probably wouldn't increase overall incomes because local institutions would be overwhelmed by new voter preferences and cultural norms. Unfortunately, it's also extremely difficult to develop these institutions in poor countries (the incentives tend to point the wrong way, see Acemoglu on the "iron law of oligarchy").
So the best donation bet might be "meta-Growth" -- attempts to increase the value of Growth by researching more effective methods of intervention to increase Growth.