Well for starters the first modern European army with commoner officers was France's when it had to take on all of Europe in 1790. So dating it to WWII is being more than a century late.

If you focus on Britain only then this was effectively turned around with the Cardwell reform of 1871: https://victorianweb.org/history/armyrefs.html (and you can find examples going back to the 17th century where "commoners" became officers in areas where competence was considered more important than anything else). As for the rest of Europe, that happened long before WW2 as well. Did you mean to write WW1? Even at that time nobility didn't have much to do with the army in most of Europe.