I started shooting/hunting with single-shots.
My dad has an old Remington .22 single shot that I hunted squirrels with (was certainly a challenge without a rear site), as well as a single-shot 20ga.
I hunt with an 870 now, but have still only needed 2 shots to get the 2 deer I've shot (1 shot each). If I can't make a good shot, I'll either pass, or wait for one.