In the course of this enquiry I found that much more had been done than I had been aware of, when I first published the Essay. The poverty and misery arising from a too rapid increase of population had been distinctly seen, and the most violent remedies proposed, so long ago as the times of Plato and Aristotle. And of late years the subject has been treated in such a manner by some of the French Economists; occasionally by Montesquieu, and, among our own writers, by Dr. Franklin, Sir James Stewart, Mr. Arthur Young, and Mr. Townsend, as to create a natural surprise that it had not excited more of the public attention.
“to’ is complex because it has different uses – sometimes the hardest words are those that look simple. In truth, the best way to try and get this right is often to “learn phrases” as it is one of those areas that the “rules” are so complex that they end up confusing you. In your example, you cannot say: “global programme to educating people.” If you want a grammatical answer, I’d say that in “global programme to educate people..” “to educate” is an infinitive of the verb, whereas in “the key to making this happen..”. the “to making” is a preposition followed by a verb meaning the “to” bit belongs to the noun and not the verb.