I was looking at different polymers and noticed that some of them have a simple enough synthesis that they could have been discovered significantly earlier.
- Phenol-formaldehyde resin/bakelite: All that is necessary to make the polymer is heating a mixture of phenol, formaldehyde, and an acid that acts as a catalyst. To make useful items, the last stages of heating need to be done under moderate pressures (a few atmospheres) since water is produced as a byproduct, and at atmospheric pressure it will boil and create tons of bubbles in the plastic, but this would be a pretty simple next step after the initial discovery of the polymer. Phenol was discovered in 1835, but formaldehyde was only discovered in 1859, so without moving back the discovery of formaldehyde I don't think it would be commercialized before 1880-1890 at the earliest. However, formaldehyde is pretty simple to manufacture and I'm honestly surprised it was discovered so late, so if it was discovered around the same time as phenol you might be able to have commercial production of Bakelite by the late 1860's.
- Cellulose acetate: Synthesis is much easier than for phenol-formaldehyde resin, you can see an example on page 134 of this book. Requires only something rich in cellulose such as cotton, and acetic anhydride (which was discovered in 1852). Cellulose acetate was apparently first prepared in 1865, but this seems to have been forgotten until 1903, and commercial production was underway by 1910. Although today it's used to make synthetic fibers for clothing, this requires the addition of plasticizers to make it more flexible and less brittle, and early products would likely be lacquers and solid objects like combs. If the 1865 discovery was exploited, it seems reasonable to have commercial production by 1875 or so.
- Poly(acrylate esters), i.e. poly(ethyl acrylate): Produced via the esterification of acrylic acid and an alcohol, (i.e. ethanol for ethyl acrylate) using an acid catalyst. Other esters like ethyl acetate were synthesized all the way back in the 1700s, and the term "ester" was coined in the 1840s, by which time the idea that there was a class of compounds created by refluxing a carboxylic acid and an alcohol in the presence of an acid was fairly well established. Acrylic acid was discovered in 1843, and can be produced via the oxidation of acrolein, probably using nitric acid at first and then catalytic routes once the process is more developed. Acrolein can in turn be produced by heating glycerin, a waste product from soap manufacture, with sulfuric acid or many other substances that act as catalysts. These polymers could be especially interesting as they are both synthetic rubbers, with a useful temperature range of roughly -10 to +150 degrees Celsius, and are also transparent. However, the polymerization is via a free-radical reaction, which means that a source of free radicals is required. This would probably start off with sunlight, but as the quantities increased, chemical initiators like benzoyl peroxide (discovered in 1858) would probably be necessary. OTL, transparent poly(methyl acrylate) was prepared in 1880, while commercial production started in the 1910's. If the initial discovery of the polymer takes place c. 1855-1860, commercial production might be possible by 1870-1875.
- Poly(methacrylate esters), i.e. poly(methyl methacrylate)/Plexiglass: Methacrylate esters are synthesized via the esterification of methacrylic acid. Methacrylic acid isn't usually prepared from acrylic acid, but instead via the hydrolysis of acetone cyanohydrin, which is in turn synthesized from acetone and hydrogen cyanide. Methacrylic acid was first synthesized in 1865, but commerical production of methacrylate ester polymers only started in the 1930's. The most common methacrylate ester polymer is poly(methyl methacrylate) with small amounts of other monomers such as acrylate esters added before polymerization to improve properties such as impact resistance, although even pure poly(methyl methacrylate) is much harder to shatter than glass. Poly(ethyl methacrylate) is apparently more flexible than poly(methyl methacrylate), and might be a good option either on its own or as a copolymer with methyl methacrylate. Since methacrylic acid was discovered later than acrylic acid, and its synthesis is more difficult to scale up due to the need to work with huge amounts of hydrogen cyanide, I think industrial production would have to wait until at least 1885-1890.