When this truck left the original manufacturer's shop (more than likely Reo or Studebaker) it was absolutely no sooner than 1949. Who may have cobbled what onto after that date at this point is anyone's guess. On the vertical surface of the frame rail between the axle housing and the fender should have a five or six digit number. This number is stamped into the frame rail, not attached to a plate. Sometimes this number begins with "M", sometimes not, depending on manufacturer. Oftentimes directly beneath that number is the manufacturing date - no code, just the simple date, sometimes in numbers, sometimes in letters (i.e. Jun 6 67). The truck has been heavily modified as rdixiemiller pointed out, with replacement windshield, and seat, addition of heater, replacement of wiring harness and instrument cluster as well as light switch.
It appears that the original bed has been removed as well. It is for an absolute fact a G-742 series truck, although there are not enough photos or information given yet to determine what type (M34, M35, M36, M45, etc.) it was originally.
On the transfer case beneath the truck there will be a ID tag for the transfer case itself. However, on trucks this old the tag was usually also stamped with the buyer's (truck manufacturer's) name - Reo or Stude, as well as the customary date. While it is possible that the transfer case was replaced in a later rebuilding, if for some reason you cannot locate the frame info, its worth sliding under the truck to take a look at this.
As an aside, since your original objective was to mod a truck into a faux WWII German vehicle, this one would be a prime candidate. This truck is too modified to be economical to restore as what it was originally, so may as well make something you want out of it!
Best wishes,
David Doyle