When it walked in from outside. UF IFAS is clear that German cockroaches do not enter structures from outdoors; they're spread entirely by people, in grocery bags, cardboard, used appliances and furniture, and between apartments. The big ones are different. UC IPM describes the American cockroach at about 2 inches, reddish brown, living in warm humid places and coming up through sewers and ground floors through damaged pipes, and the Oriental cockroach at about 1.25 inches, nearly black, living outdoors in cool damp places like garages and basements. A single one of those in a basement or a garage in summer is often a wanderer, and the fix is sealing where it came in, not a kitchen treatment.