Randall Jarrell wrote his poem, "The Death of the Ball Turret Gunner" in 1945, having recently returned himself from serving in the Army Air Force during World War II. The poem is only five lines long, so there aren't a lot of specifics, including any specific reference to the age of the gunner himself.
We do get the sense that he is young, as were most of the people who served in that war, as evidenced by Jarrell's line:
From my mother's sleep I fell into the State
The suggestion is one of instant transition from youth, or even from infancy (protected by the mother) to being in the service of the State--the government--or that the State had replaced the mother for the gunner.
The telling line for me is when he states what happened to the gunner who was killed:
When I died they washed me out of the turret with a hose.
The inhumanity of the line, the reduction of human life to being disposed of by a mere steam hose, is Jarrell's commentary on war, in my opinion.