There were many brigadier generals who started out as a prominent and wealthy citizen in their community with no previous military experience, who then went on to recruit a volunteer company with their wealth and popularity at the beginning of the war. They rose through the ranks until they became colonel of the regiment and eventually commander of the brigade. Many of those men did turn out to be ample field-grade officers or brigade commanders.
As for successful lieutenant or major generals with no military education or previous military training, N. B. Forrest and Richard Taylor are both notable. However, both 'got in' through separate paths. Forrest aficionados correct me if wrong, but IIRC, Forrest initially enlisted as a private, and because of his wealth and prominence, was commissioned an officer. Taylor was introduced through Braxton Bragg, was commissioned a colonel and went from there. Both turned out to be natural leaders.