An open-air range per se might not be a good idea in many suburbs, but a place to test fire weapons would be.
Here’s an idea that works. Take a stout cardboard box about a foot cubed. Line the inside with rubber carpet pad material, adding up to at least an inch. Glue in square sheets of this rubber so they overlap in the corners, you’ll figure it out, it doesn’t take a master craftsman.
Cut an “X” in the top about 6” x 6”. The cuts obviously go through each sheet of rubber as well as the cardboard.
Put the box on the ground, stick the muzzle into the X and fire away. Your neighbors will never hear a thing, and the ground makes a fine bullet trap.
A wheel carriage under the box raised the backstop 16 inches off the floor of the garage so I can roll it around out of the way when not shooting. I can test fire anything short of fifty cal by shooting into the end of the box of mulch. Traps the lead, also. I have made bullet traps for 9mm, 7.62x25, 9x18, and 45 acp using a tall cat litter bucket filled with rubber mulch and the top snapped on to place targets there. Shredded rubber mulch makes an excellent energy absorber. So far neighbors have not mentioned the muffled sounds from my garage.