What does Boxing Day have to do with boxing?
"terrible," 1878, from God + awful. The God might be an intensifier or the whole might be from the frequent God's awful (vengeance, judgment, etc.) in religious literature.
Wretched; miserable; inferior: cases that would never have come up but for this god-awful legislation
Extremely: Ain't it god-awful cold in here? (1878+)