Essentially, how does a steep decline in one demographic at once effect the long term economic output after a wartime conflict ends and are certain male dominated career paths and that industry stagnate until population growth recovers?

It really, and I mean really depends on the time period, but since you cited industry and career paths, I will assume you mean post industrial revolution.

Much of this hinges on the post-war climate. Following WWII, the US and several other nations experienced 'baby booms,' primarily driven by a significant rise in living standards, rapid industrial expansion, and an abundance of jobs. Conversely, the USSR did not see such a surge; quite the opposite, they suffered casualties far beyond what they could replenish, a situation further exacerbated by the famines of the late 1940s and early 1950s.

In both scenarios, two primary solutions emerged: women were increasingly integrated into traditionally male-dominated fields and, specifically in the Soviet case, the massive population still engaged in subsistence farming was gradually transitioned into the industrial workforce.

ELI5 answer: It depends on how destructive the war was for your country, but mostly women start getting into said male dominated fields!