The use of the term "farm to table" has changed over time. Its current life-style use as described in the Wikipedia article mentioned in the question seems to be a re-use of its 1915 use. This early farm to table movement was promoted by the U.S. Post Office and B.F. Goodrich; it was rated a dismal failure by the agriculture department at the University of Wisconsin, as reported in Trade: A Journal for Retail Merchants, Volume 23, in January 2016. A few articles show up from 1915 to 1919 or so in the NGram search relating to this effort.
After this period, the "farm to table" phrase refers not to the way one "ought" to acquire food and eat, but to the entire process, which may have many steps, by which food gets from the farm (including not only the vegetable farm but poultry and livestock farms) to the table, probably with interim trips to the cannery and the slaughterhouse, the packer, and the like. The various reports over the years are directed toward trying to ensure safety and quality throughout each stage of this multi-step process.
This emphasis continues to dominate the use of the term until the advent of Alice Waters and her restaurant, Chez Pannisse, in Berkeley, California. Opened in 1971, the restaurant was unprofitable for eight years or so and needed infusions of funds from friends, but always emphasized fresh from the farm, locally sourced food, and was eventually a great success that changed the views of many and was widely adopted across the country. The use of the term as a life-style value then exists side by side with its use referring to the entire process.
One NGram document from 1996 shows the direct farm to table movement in action--the cook receives a farm to table produce box in the mail:
Jul 15, 1994 - I grow fresh mint in my yard and this is a wonderful
way to use it. Love the health benefits of fresh ginger and mint!
Making it again right now! roseannpiazza from Saint James, New York /.
flag if inappropriate. I just received a "farm to table" produce box
this morning which included fresh ginger and fresh mint. I decided to
try my hand at making this lemonade. It is absolutely delicious!!
In spite of the enthusiasm for restaurants that serve locally grown food fresh from the farm and services that deliver fresh food, the vast majority of food goes from farm to table (at home or in a restaurant) via many steps, during all of which safety (as well as maintenace of quality) need to be considered and are a major focus of Federal and state departments of agriculture.
Farmers' markets have become more common, but account for a minimal part of the total food supply.
The OED, under farmer, n2 (earliest quotation 1864), has an entry for farmers market; it has no entry for farm to table, although it cites a book that includes the phrase in its title.
farmers' market n. (also farmer's market, farmers market) orig. N.
Amer. a market to which farmers bring their produce to sell directly
to the public; a building or area designed for this purpose.
Los Angeles has a large famous farmers' market established in 1934 or so.