This minor inconvenience is so prevalent that many cars include a little hole (with a jiggle valve) built into the thermostat housing, which should be the highest point in a cooling system.
Burping (so named because of the noise made by the bubbles of coolant exiting the radiator filler neck) is done with the radiator cap removed on cars without a valve. You wait for the car to warm up so the thermostat opens, and then the pressure of the expanding coolant being heated drives the air out. Or at least that’s how it’s supposed to work, anyway.
I learned a trick from an old racer that works real well to bleed that rarely leaves me repeating my work.