Quick breads (chemically leavened) which most zucchini bread recipes are, were not developed until the end of the 18th century. This took place in America, where pearlash was discovered. Pearlash is a refined form of potash, and it produces carbon dioxide gas in dough.
In American Cookery (1796 - the first American cook book) Amelia Simmons published recipes using pearlash, and we exported some 8,000 tons to Europe in 1792. (But she has no recipe specifically for zucchini bread).
Baking powder was not developed commercially until 1857 (phosphate baking powder). So the zucchini bread as we know it (a quick bread) could have been first made in America in the 18th century when housewives discovered pearlash as a chemical leavening agent.
Zucchini plants are prolific producers, so that every way it might be used was most likely explored early on.