The first Gibson Jumbo was released in 1931. It is was what would be referred to as a slope shouldered Dread, by the width and shape of the waist and the shape of the upper bout as is meets the neck. It was in production for two years, and was replaced by the fancier Advanced Jumbo, and the lower cost Jumbo 35 (J-35). Please note that despite the name, these are all slope shouldered dreads by the standard definition. Note that Gibson's slope shouldered Dreads still carry the J (as in the famous J-45, J-55, SJ, SJN) in the model name, implying Jumbo, even though they are not Jumbos by the current definition.
The Gibson guitar with the "true" jumbo shape first went into production in 1937, for a Hollywood signing cowby/actor Ray Whitley, who wanted a guitar to compete with Gene Autry's D-45. The guitar was released as the Super Jumbo 200 (SJ-200), which followed some of the naming of the other Gibson guitars of the day. The Super part is from the Super 400 archtop of 1934 and shared the 17" lower bout. The 200 was from the list price for the standard model ($200), but a lot of the singing cowboys had custom ordered instruments.
This is all from the book "Gibson Guitars 100 Years Of An American Icon" by Walter Carter. The relevant pages are 150-155.
Kostas