Do math --- or history --- much????
If they were born at the time of the stock market crash of 1929, (not really the beginning of the depression, but just for argument's sake) they would have just be turning 16 years old when the bomb fell on Hiroshima.
Now if you want to say they were the bulk of the troops in Korea, I'll go along with you.
As for calling any generation the 'Greatest' -- I think that is nonsense.
I could make the argument right now that our 20-30 year olds fighting the WOT are the 'Greatest' because not one of them was drafted. They are all volunteers. In WWII, 2/3 of the 15 million men who served were draftees, not volunteers.
My dad was born in 1930 and joined the Navy at 17 in 1947.