Sir Thomas More referred to William Tyndale as an evangelical in the early 16th century. Tyndale himself used the term descriptively of himself as well.
The movement gained great momentum in the 18th and 19th centuries with the Great Awakenings in the United Kingdom and North America. The origins of Evangelicalism are usually traced back to English Methodism, the Moravian Church (in particular the theology of its bishop Nicolaus Zinzendorf), and German Lutheran Pietism.
Actually, it goes back a bit further....
On the next day we left and came to Caesarea, and entering the house of Philip the evangelist, who was one of the seven, we stayed with him. Acts 21:8
But you, be sober in all things, endure hardship, do the work of an evangelist, fulfill your ministry. 2 Timothy 4:5
Read the Book your chosen religion assembled!!
Luke 14:23
And the master said to the servant, ‘Go out to the highways and hedges and compel people to come in, that my house may be filled.
Sure sounds like EVANGELISM to me!
But hey; I'm just a dumb Protty.
Ephesians 4:11 Douay-Rheims 1899 American Edition (DRA)
11 And he gave some apostles, and some prophets, and other some evangelists, and other some pastors and doctors,