Before Fort Sumter, the best CSA strategy for its survival was to do nothing (OK, mobilize and build fortresses) and try hard not to give the USA an excuse to attack it.
The Constitution is silent on secession, and the standing USA army was small, so even if Lincoln was determined to conquer the CSA he needed an excuse. Once the stand-off had lasted long enough, he was more likely to give in and negotiate exit terms than to try to build an army to reconquer the South, which if the CSA wasn't doing anything was so far outside Constitutional norms that the attempt probably would have brought impeachment proceedings, even in a Republican controlled Congress. Even after the bombardment of Fort Sumter, the attempt to "suppress the rebellion" brought four more states into the Confederate camp, states that had before considered and rejected secession. Yeah, they wouldn't have brought in the Upper South, but a purely Lower South CSA that dared the federal government to suppress it could have survived.
Following Fort Sumter, they were screwed. Actually, their best strategy for the resulting war was the IOTL one, with the following exceptions: 1) put a much greater priority on the defense of first Fort Donelson and then New Orleans, cancelling the Shiloh attack to keep the latter properly garrisoned 2) much better leadership of the Army of Tennessee (don't use Bragg, who seems to have had severe PTSD, in a combat command, the same applies to Hood late war, also for health reasons), 3) keep the Army of Tennessee in the Mississippi Valley to defend that, no invasion of Kentucky, and put a Vicksburg-sized garrison at Chattanooga plus cavalry to serve as a speed-bump, and 4) no cotton embargo. This sounds like a lot, but they got pretty much everything else right, and doing everything right would have kept them alive until 1866 at the latest. Organize an army, defend key points, and hope to get either really lucky or to get other countries as allies.