The Romans used large quantities of wooden barrels, especially for maritime trade. In unchanged form this container continues in use to the present day. Papyrus' from which the word paper originates is an altogether different material, being formed by laying down a cross pattern of strips of papyrus leaves, wetting them and drying to form a sheet material suitable for writing or printing on. It predates paper by a couple of millennia. What are today accepted as being plastics, the synthetic polymeric materials, have been around for about 80 years, although some special materials such as celluloid and 'Parkesine' anticipated these by another half century.
Early dates are, of course, very approximate, and forms of 'packaging' conjectural but likely.
With the feudal systems a minority of wealthy individuals required containers for the transportation and protection of their goods. This in turn, plus the industrial revolution of the 18th and 19th centuries gave rise to a large middle class. Wider emancipation, education and political enfranchisement brought us to the beginning of the 20th century ripe for a less violent but no less significant social revolution. The adage 'necessity is the mother of invention' is certainly true of packaging, with military imperatives providing the impetus for many of the most significant developments. Incidentally, scientists working on radar had apparently discovered the heating properties of the magnetron and used this to warm their food for years, long before the microwave oven hit the market in the early 1980s.