“ The Theory of Moral Sentiments is a 1759 book by Adam Smith.[1][2][3] It provided the ethical, philosophical, psychological, and methodological underpinnings to Smith's later works, including The Wealth of Nations (1776), Essays on Philosophical Subjects (1795), and Lectures on Justice, Police, Revenue, and Arms (1763) (first published in 1896).”
It's also mentioned once in A Theory of Moral Sentiments, and in the posthumously published Essays on Philosophical Subjects, a book on astronomy. In both it's clear from context that the "invisible hand" is some unknown mechanism, and not an explanation, but a statement of ignorance. "The invisible hand of God" would be a more common contemporaneous phrase, in the sense of a Creator and Organiser of the Universe, though Smith as with Hume seems to have been largely non-Deistic.
From Moral Sentiments:
The produce of the soil maintains at all times nearly that number of inhabitants which it is capable of maintaining. The rich only select from the heap what is most precious and agreeable. They consume little more than the poor, and in spite of their natural selfishness and rapacity, though they mean only their own conveniency, though the sole end which they propose from the labours of all the thousands whom they employ, be the gratification of their own vain and insatiable desires, they divide with the poor the produce of all their improvements. They are led by an invisible hand to make nearly the same distribution of the necessaries of life, which would have been made, had the earth been divided into equal portions among all its inhabitants, and thus without intending it, without knowing it, advance the interest of the society, and afford means to the multiplication of the species.
https://en.wikisource.org/wiki/The_Theory_of_Moral_Sentiment...
Gavin Kennedy's scholarship on the Invisible Hand question is the best I've found. See his paper here: (freely available PDF download):
https://econjwatch.org/articles/adam-smith-and-the-invisible...
https://econjwatch.org/File+download/252/2009-05-kennedy-wat...
Gavin Kennedy's blog also has futher discussion: http://adamsmithslostlegacy.blogspot.com/
(Kennedy himself died in 2019.)
There are two other occurrences of "invisible" in Wealth of Nations, both occurring in discussion of warfare:
[T]he noise of firearms, the smoke, and the invisible death to which every man feels himself every moment exposed as soon as he comes within cannon-shot, and frequently a long time before the battle can be well said to be engaged, must render it very difficult to maintain any considerable degree of this regularity, order, and prompt obedience, even in the beginning of a modern battle. In an ancient battle there was no noise but what arose from the human voice; there was no smoke, there was no invisible cause of wounds or death. Every man, till some mortal weapon actually did approach him, saw clearly that no such weapon was near him.
https://en.wikisource.org/wiki/The_Wealth_of_Nations/Book_V/...