Wikipedia's own entry gives no dated origin claim for the dish itself; the only date in the article (1979) is Hans Wehr's dictionary entry for the WORD bābā ghanūj, not evidence of when the dish itself arose.
What would resolve this A food-history source (e.g. Gil Marks or Charles Perry) dating the dish, as opposed to the term, to a specific period or century.
Openfood historyBaba Ghanoush (Wikipedia)