I was recently reading a thirty year odd old book about East Stirlingshire, which claimed that the first mention of the club in the press was of a friendly against Dunipace on the 19th of November 1881 [and I will gloss over the fact that the author had missed a report of Armadale v East Stirlingshire in the midweek Falkirk Herald dated 3rd November], but this entire mistruth comes from the fact that the author had clearly only used the Falkirk Herald as a source.
Every football match takes two teams, and so it was that there was an earlier report of an East Stirlingshire match which exists not reported in the Falkirk Herald. Nearly a month before any mention of East Stirlingshire in the Falkirk Herald the West Lothian Courier of the 15th October 1881 carried this:
Armadale v East Stirlingshire
Played at Falkirk, and after a very pleasant and well contested game, resulted in favour of Armadale by two goals to nothing.
I am not saying this is the earliest mention of ESFC in the press, I am simply saying that this is the earliest I have found, and I welcome anybody who revises it to an even earlier date.