The SEC was founded in December of 1932, so the first football season was in 1933. Mississippi State's first ever win in the SEC was in '33 against Sewanee.
On the chance that you are wondering who in the world Sewanee is, let me briefly let you in on what little knowledge I have about them. They are referred to now as 'The University of the South', located in Sewanee, Tennessee. Basically, if you're taking the scenic route from Chatannoga to Nashville you'll stumble across a college in the middle of nowhere.
Sewanee is a private, Episcopal university who was a member of the SEC from 1932-1940. They didn't have much luck as they lost every single SEC game they ever played in with a total margin of 1,163-84....ouch. They now compete in Division III.