IMHO, a few days/months should not be a problem. priming is a good idea if it has been sitting not running or empty for months/years. or installing a new pump out of the box.

I worry more about lifter bleed down when they sit for extended time (months/yrs) pump always pumps oil on start up but lifters clatter till they get pump back up and full of oil.

if you have a mech oil gauge you will see it fire off and a couple seconds later you see the psi shoot up. that's the time it takes for oil to go thru pick up tube/pump/filter/passage to sender port. then on too lifter galleys.

stock electric oil gauge may be a little slow to react and only seem to take longer. this is why I prefer a mech gauge. reacts faster on start up. if there is no oil flow you see it right away.