The shattered manufacturing capabilities of Europe put the US in a leading position to be the primary provider to take its place. Essentially Europe was gone as a competitor in the global economy and became a consumer. This led to massive demand in the US which of course led to companies paying lots of workers to fulfill it.

> If anything, the most immediate outcome of the victory is a sudden influx of unemployed soldiers needing jobs, which causes downward pressure on wages.

You had fewer soldiers coming back than you had shipping off. You also had worldwide demand for manufactured goods to meet, and Europe lost basically its entire infrastructure and nearly an entire generation of working age men.

Good points

What the parent is referring to is the US having industrial production capacity that was left intact while Europe was in shambles.

Yes, that is one factor, and perhaps the parent was referring to that, but if so I don't feel that "simply because they won the war" expresses that particularly clearly.