score:3
Having done some more research, the Wikipedia article on Evangelicalism and this overview by the Gospel Coalition suggest the following timeline for the term coming into use:
1500s: Protestant reforms use the word "evangelical" in its literal meaning: the greek word meaning "gospel". This was to emphasise their message based on what they saw in the Bible.
1600s: In the wake of the reformation, a number of different movement appeared across Europe, such as Pietism and Calvinism, each emphasising different aspects of the reformation.
1700s: British and American reformers start to combine elements from all these different movements into movement, and take on the word "evangelical" that was used by the original reformers. In part, this movement was motivated by a renewed assurance in their faith, and in part a natural outcome of the changes happening in wider society.
I suspect this brushes over much of the historical nuance, but appears to serve as a general overview.