It was far from a lost cause. Only through an all out deployment of resources, which is what the war became, can the Confederacy be considered a lost cause. But wars rarely become total in that fashion. The Napoleonic Wars, the most common point of reference at that time, had mostly been decided by set-piece battles and quickly negotiated treaties.

The Confederacy had to hold out until 1864, when Abraham Lincoln came up for re-election. Lincoln would not rest until the Union was restored, but he was in fact heavily disfavored until almost the eve of the 1864 election. Military victories such as the fall of Atlanta sustained him at the last minute.

Lincoln's challengers mostly promised a negotiated peace with the Confederacy. If one of them had won, America would have almost certainly been divided.

The Confederacy did have all of the advantages you mention, especially in the east. While they had a string of victories in the east, they had a string of failures in the west. The early Union victories along the western rivers may have kept Lincoln from being swept out of office early. He himself wrote to army commander William Rosecrans after the 1862-3 Battle of Murfreesboro, TN, that "you have given us a victory at a time when a defeat the nation could scarcely have lived over." By 1864, Union leaders in the west had captured Kentucky, Tennessee, Mississippi, and Louisiana while Union leaders in the east had advanced barely 50 miles into Virginia.

The Confederates were outnumbered and outgunned in most of the major battles of the war. That's a disadvantage that can't be discounted. But in sum, they certainly had a number of chances to win the war if they had managed to win a lot more battles in the west or if they had won one or two more battles in the east.