To be honest, Sam ended up being one of the co-authors of the ultimate tome of Westerosian history, A Song of Fire and Ice, so we’re willing to believe that the man was able to invent plastic way sooner than that of our normal realm.
In the middle of discussing whether or not Jon Snow should live, and making Bran “The Broken” Stark king of Westeros, there was a plastic water bottle behind Samwell Tarly’s left leg.