Sn act of Providence means an act of God expressed in this way so as not to disturb those who don't like to talk about God

In this context, I believe the author uses 'providence' to mean an act of God. Translated to a non-religious context, it might be "A stupid man is born a stupid man by pure chance".

I generally liked this PDF but disagreed with this part. I’ve seen intelligent people become stupid depending on the context and vice-versa.

In this context, "Providence" likely refers to a deity, which is indicated by the capitalization of the word.

The word "Providence" means "an influence that is not human in origin and is thought to control people's lives", or "God conceived as the power sustaining and guiding human destiny", or something like that. It does not mean "prudence" or "provision of care", usually.