When Superman debuted in June 1938, we were informed that "nothing less than a bursting shell could penetrate his skin". While his powers of resistance grew substantially over the next few years, even his initial description put him at the pinnacle of superheroic toughness in that point in time.
So lets say you're a dastardly villain, looking to protect your "legitimate business" or "diplomatic investigations" from some meddling do-gooder. Maybe it's not even Superman, maybe it's the Blue Beetle with his bullet-resistant mesh costume. Maybe it's Wonder Woman or Namor or Captain America with his annoying shield. What are your options?
Well, outside of mad-science death rays or superpowers of your own, they're surprisingly limited. American military research seems to have stagnated pretty hard in the 1930s. A bunch of America's iconic World War 2 weapons were only developed when we entered the war, or maybe a year earlier. Bazookas, Sherman tanks, flamethrowers, dedicated antitank guns... none of those existed in the United States in 1938. So let's see what was around.