A bit more information about the picture (originally [as well a repeatedly] posted on Reddit):
"Corporal Luther E. Boger of US 82nd Airborne Division reading a warning sign, Cologne, Germany, 4 April 1945"

Most likely hand-lettering...

You think? Some of the repeated characters look pretty much identical to me...

I agree with Nick.
Also, consider the size of the letters. I can't see a letterpress machine with huge fonts in a battle zone in WWII.
On the other hand, I expect that some soldiers had sign writing/showcard experience could have whipped this up. Many took pride in the regularity of their lettering. They would use many sources as their models. The lettering is a pastiche of easy to draw styles of the era.
The F in "Fighting" is interesting. A source font?
Don