we get an annoying growling noise when we start up the car after it sits

A "rumbling growl" suggests a bad bearing on something like the water pump, idler pulley, or alternator, or perhaps something from the road caught behind a pulley. It is very unlikely it has anything to do with with oil pump, since a failure there would destroy the engine very quickly.

I had this problem. Honda issued an extended warranty on the engine and I took my car in to have them check it (although I had complained about this for years) to test the engine, they changed the oil and told me to check it every time I put gas in the car. It turns out the oil was gone in a week (or less) due to the piston rings. They thought they only had to replace the seals on the rings....but the damage was so severe they had to replace the pistons. Finally,, the grinding roar is gone ☺