The firing on Fort Sumter is a lot more several minor mistakes with a catastrophic chain reaction than a deliberately provocative element, and so could occur at any federal facility on rebel soil (Harpers Ferry Arsenal, St. Louis Arsenal, Norfolk Naval Yard, the New Orleans forts, or if Maryland seceded as it nearly did, the completely surrounded Washington DC.) But the later it occurs, theoretically the better organized the Confederate Government and industry becomes.
If Missouri seceded as it nearly did being about evenly split, the Confederacy controls far more of the Mississippi as well as the Missouri River-the superhighways of the pre-western railroads era. Missouri had already developed sizable lead and iron mines, walnut forests (gunstocks), and raised a lot of food. St. Louis was a key federal strongpoint and westernmost arsenal for that matter. It probably creates much more of an Upper Midwest battlefront that perhaps breaks away pro-secession Southern Illinois like West Virginia and Virginia split then. With Chicago's rail hub threatened, that would drain Federal troops considerably to this new vast front, the Copperhead strategy of 1864 but in 1861 instead.
Maryland having extra time to decide to secede might do the trick and would add substantial manufacturing capacity to the Confederacy along with the Chesapeake Bay port advantages (and of course the disruption of DC as the federal government packs up and flees, perhaps it becomes the Confederacy's capital instead of Richmond, certainly the buildings are already there. The Naval Academy at Annapolis is lost too.
Assume Kentucky joins a more organized Confederacy with more time to think about it and campaign internally. That changes the Ohio River Valley corridor access and moves the battlelines further North. As John Keegan points out, when you taken into account the main rivers as the logistics corridors/avenues of approach, the Civil War's conflicts and lack of progress make far more sense.
Drawing on the newest histories of the Knights of the Golden Circle movements, with only a month or two's delay, the assembling military expedition in Texas (1860-1861) under the Knights of the Golden Circle leadership to putatively go assist Benito Juarez's forces in kicking Maximilian out of Mexico for the eventual repeat of how Northeastern Mexico became Texas might well proceed rather than turn East and become the early, already drilled and equipped units of the Confederate Army.
Arriving instead in Northern Mexico with 10-30,000 troops under often commanders who'd fought 14 years before in Mexico, as well armed if not drilled as the Austrians and French troops/commanders but considerably ahead of the Mexican resistance, they might have won and likely turned on Juarez and kept much or all of Mexico. Conquering all of the countries along the Gulf of Mexico and Cuba to make them slave plantation states was the overarching goal of the KGC for decades of filibustering expeditions and schemes.
So drawing off what would have been the nucleus of the Confederate Army into Mexico until 1863-5 defangs Confederate saber-rattling considerably. Napoleon III's otherwise very sympathetic regime to the CSA is lost as an ally, apparently he planned to ally as soon as Britain did from Amanda Foreman's "A World Set On Fire."
But with the choice between a battle for plunder and conquest in Mexico vs. a defensive war fought on one's own homesteads with only degree of loss at stake, I think the CSA's population would have taken the far more attractive option.
The North's radical abolitionists, a minority, would still be wrestling with the financial interests in New York where the dollars for Southern agricultural commodities sale and financing passed through as a huge part of the NYC economy as well as the feedstock for New England's textile mills, cigar factories, apparel makers, rum distilleries, etc..
Lincoln's lack of a clear majority and reliance on a political party of recent origin would make governance even more challenging without a clear, unifying foe like the CSA (and he would also flirt with supporting Juarez in Mexico with either troops or at least supplies, sending tens of thousands of U.S. Army rifles to Juarez in 1865.)
The new western railroads were already being planned and proposed to knit the coasts together and keep the CSA from taking Colorado, Montana, California, Arizona, Utah, etc. so without an open war, those projects likely get advanced 3-10 years ahead of OTL-particularly the Union Pacific, Central Pacific, Kansas Pacific, and Northern Pacific railroads which draw off much of the available financial capital and workforce who'd have otherwise been soldiers.