Plastics have been used many centuries ago in the form of bio-derived materials such as egg and blood proteins. But the major boom occurred when back in 1839 Charles Goodyear accidentally discovered the method to vulcanize rubber. Vulcanization is a processes which strengthens the rubber and makes it more flexible and durable.
Later on, 1846, a Swiss chemist named Charles Schonbein accidentally (again) discovered how to produce the plastic polymer known as celluloid.
In 1909, chemist Leo Baekeland created Bakelite. Bakelite was the first true synthetic polymer that could be put into molds and shape it into solid objects.
Nylon was not invented until 1930s. A chemist named Wallace Carruthers is the man who invented this marvelous type of plastic.