Militaries have been using full length stocks with metal tips since the advent of the shoulder arm. Barrels were expensive, wood was cheap.

When I first became enamored with Mannlicher-Schoenauers a few decades ago while in Germany, I looked into the history of the "stutzen." The first thing I found out is that the term is most often used in regards to support hose (stockings)

Further research led me to believe that the first time the stock style was applied, as we know it today, was with the German M88 Cavalry carbines of circa 1890. An example is below, stolen from the mentioned website.

You can cleary see the lineage that led to Mannlicher-Schoenauer hunting carbines 10 years later. Of particular interest to me has been the stutzen rifles (hence my email address). These are 23.5" barrels with full length stocks. Both M-S and Brno made them for the cartridges they deemed to powerful for short barrels, with Brno it was the 7x64 and the 8x60S. With M-S it was mostly the 9.3x62. Below is an 1950 full stock rifle in 9.3x62, made in 1957. Below that is an NO in 9.3x62, made in 1959 (sorry for bad photo, I know longer have the rifle to take a better one).

This one is a Brno 22F rifle in 7x64, made in 1946.