During the American Civil War many of the late war officer corps were extremely young for their rank. This was a result both of the heavy attrition suffered by Union forces and the constant need for rebuilding and expansion following the defection of many members of the army. Some of those officers did rise from either the enlisted ranks or from the bottom of the officer chain.
One such was Elisha Hunt Rhodes, a Rhode Island man who survived the entire war. He began his career as a private in the 2nd Rhode Island Volunteer Infantry and eventually rose to command of the regiment as a colonel serving under General Sheridan in the Shenandoah Campaign. Much of his journal and many of his letters are compiled in All for the Union : the Civil War diary and letters of Elisha Hunt Rhodes. It's a widely available and very readable account of the war.
It was actually, some what common for relatively obscure, indistinct men to be given high commands in Nazi Germany, especially near the end of the war.
There was the case of Leon Degrelle. He was a minor Walloon politician and university dropout, when the Germans invaded they created a collaborationist unit called the Walloon legion. Degrelle joined as private in 1941. By February 1942, he had been promoted to Sergeant, in Winter of 1943 he helped stop an encirclement of German troops and was promoted to commander of the Walloon unit. He was given numerous decorations and high praise by Hitler.
Also, some of the Nazi generals were given high ranking commands simply by being loyal to Hitler. sepp dietrich was given command of two Panzer armies, despite having very little command experience, and starting out as Hitler's bodyguard and enforcer.
The French Revolution and First Empire probably give you the most examples. Masséna, Murat, Ney, Soult and Lannes were all enlisted men who rose to the Rank of Marshal.
But the most complete rise in history must be Jean Bernadotte, he enlisted in 1780 as a private soldier in the pre-revolutionary French marines, was stationed in Corsica and was made a sergeant in 1788. In 1790 he faced down a mob in Marseille to protect his colonel. At the end of 1791, he received a commission as a lieutenant.
He fought throughout most of the major battles of the Flanders campaign in 1793-95 ending up a général de division and the military governor of Maastricht. He then came under the command of Napoleon during the campaign in Italy in 1797, and married Désirée Clary, whose sister was married to Napoleon's brother Joseph.
After Napoleons rise to power he held a series of important civil, diplomatic and military posts and became a Marshal of the Empire in 1804. As a reward for his services at the Battle of Austerlitz he was made the 1st Sovereign Prince of Ponte Corvo.
He was then (somewhat unexpectedly) elected as the Crown Prince, Regent and heir apparent to the throne of Sweden. He Joined the coalition against France in 1813, defeated Norway in 1814 and became Charles XIV John in Sweden and Charles III John in Norway in 1818.
The 'House of Bernadotte' are still the current royal house of Sweden. And Bernadotte remains probably the only European crowned head of state to have 'MORT AUX ROIS' or 'death to all kings' tattooed on his arm.
I've removed this as a "throughout history" question: all you're getting here is trivia about individual people who rose through the ranks, and no analysis about whether it was common practice.
It's this text which makes it a "throughout history" question:
I'd be more interested in 19th - 20th century(inclusive) examples but I'd also be very happy with answers pertaining to any part of history.
What, exactly, are you trying to learn?