Street food culture is independently attested in the ancient Roman world (popina and thermopolia, over 80 counters excavated at Pompeii) and has since developed independently in virtually every urban culture. No source consulted names a single point of origin, and the phenomenon is defined by a recurring urban condition (city dwellers without home kitchens) rather than a single invention or diffusion event, so an honest origin-start-year cannot be given without implying a single-origin claim the sources do not support.
What would resolve this A comparative food-history source establishing whether ready-to-eat food-for-sale independently arose in multiple ancient urban centers (Rome, and separately in ancient China, Mesoamerica, South and Southeast Asia) on convergent timelines, or whether the earliest attested instance anywhere (not just the Roman world) can be dated and cited.
OpenFood HistoryAncient Pompeiians Stopped at This Snack Bar to Feast on Snails, Fish and Wine (Smithsonian Magazine)