Exactly as the title says, what would happen if the Confederates never fired on Fort Sumter? Would the Civil War start at all if they didn't? Could the Confederacy have survived if they hadn't attacked the fort?
Not firing on the fort was a distinct possibility. Confederate Sec of State Robert Toombs had been a noted "Fire-Eater" (secessionist radical) before the war. But when Davis met with his cabinet to discuss Fort Sumter, Toombs strongly - even passionately - advised against the attack.
"Mr. President, at this time it is suicide, murder, and will lose us every friend at the North. You will wantonly strike a hornet's nest which extends from mountain to ocean, and legions now quiet will swarm out and sting us to death. It is unnecessary; it puts us in the wrong; it is fatal."
Toombs had also been an early favorite for President of the CSA; he withdrew his name because he mistakenly thought fellow Georgian Herschel Johnson wanted the job.
If he was President, he would not order the attack.
So what happens? The garrison was very short of food (Anderson admitted to a Confederate delegation that "We will be starved out in three more days"). If there is no attack, that's what happens.
Lincoln is not going to proclaim a state of rebellion and call for troops as in OTL. So Virginia is not going to be pushed into secession, nor Tennessee, North Carolina, or Arkansas.
There remains a bone of contention: Fort Pickens, at Pensacola Bay in Florida. Unlike Fort Sumter, Fort Pickens is outside the bay with uncontested access to the sea; the U.S. could resupply and reinforce it.
Davis felt compelled to force the issue with Fort Sumter because it sits in the mouth of the harbor of a major Confederate city.
Fort Pickens is more out of the way. It can block Pensacola Bay, but Pensacola is a minor city. The CSA can ignore it if they choose. Floridians may be annoyed, but it's not going to be the flashpoint unless someone makes it so.
Another point is that Fort Pickens is not where the CSA can get at it effectively. It's at the western end of Santa Rosa Island, with a narrow spit leading off to the east. To the west and north are the open waters of the Bay; to the south is the ocean.
So a cold blockade seems likely.
The question is how long the "sitzkrieg" lasts. The CSA will be pressing secession on the upper South, and Lincoln will be intriguing against them.
Virginia is key. OT1H, most Virginians either oppose secession or don't want the state to be a battleground. OTOH, Virginia is a slave state, with its own Fire-Eaters such as Roger Pryor. One possibility - there was a plot by some Fire-Eaters (including former Governor Wise) to seize the Navy Yard in Norfolk and the Harpers Ferry arsenal. It was pre-empted by the attack on Fort Sumter, Lincoln's proclamation, and Virginia's declaration of secession.
If no Fort Sumter attack, the plot goes forward. It would probably fail, and could turn popular feeling against the CSA; Virginia might not secede.