Has an Euros game ever ended 4-0?
It has. 4-0 has been a Euros final 5 times in 388 games. The first was Spain beat Republic of Ireland on June 14, 2012; the latest was England beat Ukraine on July 3, 2021.
That makes 4-0 the 11th most common final score out of 20 that have ever occurred in Euros. One point away, 5-0 has happened 4 times and 4-1 has happened 6 times. Nearly all of its occurrences fall between 2010 and 2039.