Buying a 16-inch gun design does not create the gun

Could Germany have bought American or Japanese 16-inch gun designs before the Second World War instead of using 15-inch weapons?

The drawings could be acquired, but Germany still needed the machinery, metallurgy, and production experience to manufacture the larger weapon reliably.

A technical drawing is only one input to a major naval weapon programme. The factories must be able to forge, machine, heat-treat, assemble, and test components at the required scale. Germany chose a 15-inch weapon partly because it could actually construct it. This answer pairs well with the later large-gun discussion by showing why paper access does not instantly bridge a lost or absent industrial process.