In Saving Private Ryan, Tom Hanks's Captain Miller is the consummate leader--respected by those both above and below him in the ranks, brave and skilled. How likely would it have been in World War II for a small-town English teacher--a draftee? A volunteer?--to reach that rank and that level of success in the Army, and what would have gone into making that happen?
Captain in the Army actually isn't anything particularly difficult to achieve assuming you're joining as a Second Lieutenant; all you have to do is not screw up badly and you'll be automatically promoted to captain, it's Major where you actually have to start competing.
Keep in mind that an Army/Air Force/Marine Corps Captain is the equivalent of a Navy/Coast Guard Lieutenant, a Navy/Coast Guard Captain is the same rank as a Colonel.
I'm sure if he had volunteered with a college degree, it would not have been out of line to see him with a commission as a Second Lieutenant, and if he made it all the way to D-Day, promotions must be made as superiors are KIA/MIA. Everything just depends on the timeframe.