During the first month of fighting, how many battles had
Gálvez and his troops lost?

The correct answer is he has lost 0

Explanation:

"In August 1779, Spain finally declared war on Great Britain and Galvez was free to act openly. He knew that his best chance of success was to strike first by surprise. Within a month, he had captured all four British forts in the lower Mississippi including Baton Rouge and Natchez. He captured 550 enemy soldiers and two naval vessels, one of which was captured from land. . . . He did this all without suffering a single defeat. His success was even more remarkable because a hurricane had sunk his supply ships." In this it states that he never suffered a single defeat.

"the royal proclamation of 1763"