First bicycle - This depends on one’s definition of bicycle

First bicycle ridden off road: This depends on one’s definition of bicycle. In 1816 Baron Karl von Drais built what came to be known as a draisine. He rode it in the forests of the Duke of Baden as the duke’s “Master of Woods and Forests”.
First bike with pneumatic tires ridden off road: In 1887, Irish veterinary surgeon John B. Dunlop fitted a piece of rubber hose to his son’s bicycle. The superior air suspension this provided over solid tires led to world-wide acceptance by 1891. Tire sizes were commonly 30 x 1.5” and 28 x 1.5”. No doubt, bikes with these tires were ridden on dirt, as there were few paved roads.
•  First bike with fat tires ridden off road: The “fat tire,” that is one having a cross-sectional diameter of 2” or more, is what later fired the imagination of so many to how far a bicycle could go off road. It gave the mountain bike its extreme degree of ruggedness. Bicycle fat tires, also known as balloon tires, came into existence in the early 1930s, possibly late 1920s. Whether the first balloon-tire bike to be ridden off road was American or European (possibly German), I don’t know. Semperit had a 26 x 2” tire in the early 1930s. Arnold, Schwinn & Co. of Chicago was introduced to such a tire in Germany in 1932 and popularized the size in America.
•  First fat-bike with a derailleur ridden off road: As far as I know it was Russ Mahon of Cupertino, California (75 miles south of Marin County), who came up with this combination, in 1973. He grafted derailleurs onto a 1930s balloon0 tire bike built by the Cleveland Welding Company. He also put thumbshifters on this bike. Three Cupertino riders including Mahon showed up at a Cyclo-cross race in Marin, December 1974, pollinating Marin with these ideas. They then departed the scene for more than 20 years
•  First fat-tire bike with a derailleur and good brakes: Again, as far as I know, it was Russ Mahon’s bike. In 1973 he put front and rear drum brakes and motorcycle brake levers onto his bike.
•  First fat-tire bike with a derailleur and good brakes in Marin: Gary Fisher’s 1938 Schwinn-built B.F. Goodrich (Excelsior-type), Fairfax, California, September ’74 or summer ’75. This much-photographed bike is equipped as it appeared in late 1978, but it is basically circa 1976.
• First fat-tire bike with a new frame and all new parts: Breezer # 1, frame and bike built by Joe Breeze for himself, Mill Valley, California, (Marin County), Oct. 1977. This was one of ten Breezers I built at the time. The frames were built of straight 4130 large-diameter, thin wall tubing. The term “clunker no longer applied to all bikes ridden on Mt. Tam.