In 1856 Alexander Parkes patented "Parkesine" the first member of the celluloid class of compounds.
This is considered the first man-made plastic.
Depending on how you wish to define "plastic" you can go even further back than that.
For example in 1844 Thomas Hancock in Britain patented the vulcanization of rubber (think car tires) and Charles Goodyear patented it in the USA in the same year
In 1839 Eduard Simon, a German, discovered polystyrene
Around 1000 BC is the first historical evidence of the use of shellac.
Source: https://en.wikipedia.org/wiki/Timeline_of_plastic_development
So plastic and its derivatives or components have been around for a long time (hmm wonder if any of those water bottles are still decomposing LOL) depending on how picky you want to be about the term