Im not really sure, not that much insignia on him.
Of course hes gonna be with the Soviet forces, and as you said he was born in Ukraine, so probably a Ukrainian battle group?
He was private in (probably) construction troops or signal corps (not sure which one - details are blurred).
He had "ready for work and defense" military sportsman badge.
His shoulderboards have a bit unussula shape, so maybe it's his picture from the time he was about to be demobilized.
I would say that the picture was taken between 1955 and 1969, with 1955-1960 being more probable (metal buttons on his gimnasterka). If he was born in 1940, than this photo would have been taken between 1958 and 1960 most likely.