I don't have one of those cooling system vacuum filler kits but if you do, that is the easiest most efficient way. I use a method that has worked for me, time and time again. Jack up the fill area, radiator or coolant reservoir, radiator in this example. Jack up the front end about 6 inches at least or put the front end up on ramps. Then, with engine not running, fill the coolant very slowly. when you get coolant showing up at the radiator neck, start the engine and turn heater on and let run for 2-3 minutes and then again, fill very slowly. When you see coolant again, set the vehicle level and top off if needed and make sure the thermostat opens. Then roadtest and recheck and add as needed.
When I did my 2005 Tahoe water pump, I followed this method and ran the right front tire up on a ramp.