Eisenhower had the "benefit" of two world wars to enhance his promotion speeds. Going by those dates, he was commissioned a 2LT in 1915, and became a 1LT a year later. Quick, but that is historically a fairly quick process. The jump to CPT was extremely fast, but note that it occurs the month following US entry in to World War I. This isn't too surprising, because with the sudden need to enlarge the military and bring in vast numbers of raw recruits, existing officers were the best bet the army had for leading the increased number of commands suddenly created, and promotions were the result.

His next two promotions, to MAJ and LTC, were temporary wartime promotions, to allow him to lead his various assignments. They weren't permanent ranks, and after the war ended, he reverted to his official rank of CPT. His service during the war was deemed excellent, so he was quickly then promoted officially one step again, to MAJ.

Eisenhower sat at MAJ for 16 years, significantly longer than one would ever find a person in that rank now. During that time he worked as a staff officer for several important generals, and attended important military educational programs, eventually earning promotion to LTC.

His remaining promotions came during the build-up to, and conduct of, World War II. He had, by this time, been identified as a highly capable staff officer, and the opportunities that arose in the once again massively expanded army, combined with his competence in carrying out assignments given to him, served to elevate him through the general ranks.

Sourced largely from the US Army official brochure about his career.