starting the engine after it's been sitting for a while is pretty much the same for the bearings whether the pump is primed or not.
it's going to take a couple of rpm after the engine starts running in order to get the oil pressure up and pressurize the bearings.
the usual solution in a race car is to put an additional switch on the ignition so you can spin the crank over with the starter motor until you see good oil pressure on your gauge ( < 5 seconds ) and then you light the engine off. usually a race car will actually have two switches, a momentary switch to run the starter and a rocker switch or toggle to turn the ignition off and on.
for a street car like you've got in which you're only trying to make sure you've got prime on the pump again and you're only going to do this once in a blue moon, pull the spark plugs out and at least one of the valve covers off.
removing the plugs gets rid of compression and makes the engine much easier for the electric battery / motor to spin the crank. it also gets rid of the spark so the engine can't fire off.
pulling the valve cover allows you to verify when the rockers are getting fed with oil. the rockers are both the highest oiling point in the engine and also the furthest out in the oiling circuit so by the time that the rockers are taking a good amount of oil you can be sure that the whole system is primed and pressurized.
spin the crank for ~30 seconds and check the valve train for oil. repeat as necessary.
once you've got oil feeding, put the valve cover back on and your plugs back in and you're ready to go.