There's a large possibility that it used to belonged to his grandfather. Remember how he found his grandfather's notebooks and a 축구 ball when he was helping Atsuko cleaning up for New 년 when he was a kid? Maybe he found it among his grandfather's soccer-related stuff too.
posted over a year ago
Oh, God! I think episode 121 showed how Endou got his headband! Around 분 6-8.