We all know that didn't have its origins until the Nixon years and didn't blossom until thereafter; i.e., during the Reagan years. But how might it have happened earlier? One thought, although bordering on ASB: somehow, the Wallace forces hijack the 1948 Democrats' convention, putting former VP Henry Wallace (instead of Harry Truman) at the top of the ticket, with Idaho senator Glen Taylor as his running mate. The Dixiecrats led by Strom Thurmond and Fielding Wright would still bolt, perhaps even more vehemently given the Wallace nomination. Now, if the GOP nominates Ike (with perhaps Earl Warren as his VP nominee), we have the seeds: I could see Texas looking at Wallace and deciding he's not right, and the same for Thurmond (too much the "old school"/eastern deep south; doesn't speak for Texas). That would leave Texans (and by extension, Oklahomans and Arkansans (?) to vote for Ike, thus causing the first cracks in the Solid South.
Once the first chinks in the armor develop, it shouldn't be difficult to make further inroads--say, in VA, KY, or TN. Alabama, Mississippi, and Georgia would still be the last to fall, but they might by the 1960s.