'bang-up' originates from English, specifically the elements 'bang' + 'up', where 'bang' is an imitative/onomatopoeic word for a sudden loud noise and 'up' functions as an intensifier or directional particle.

'bang' (an imitative word recorded in early modern English) combined with the particle 'up' in colloquial compounds in the 19th century; the compound 'bang-up' emerged in informal English to describe something done with a 'bang' or with notable effect and was used in phrases like 'bang-up job.'

Initially tied to the literal idea of a forceful 'bang' (and to damaging or striking), the compound gained an extended colloquial sense of 'remarkable' or 'first-rate' by the late 19th/early 20th century; both senses (damage and excellent) coexist in informal usage.