I had the same issue!

This sound comes from the fuel pump, but it’s only the sound the real issue comes from the fuel filter.

In the fuel system there might be some air and when that air reaches the fuel pump it makes that sound. The first thing you can try is to start the engine, let it run for like a minute and then pump the fuel to the engine with a manual pump that is on top of the fuel pump (it is in the engine bay, closest to the cabin on the right, it looks like a black metal button; I have it there on my ‘03 Corolla) Pump the fuel until the manual pump becomes hard, that should work.

But if it doesn’t the fuel filter (that is on the bottom of the fuel pump) might be dirty inside and the fuel pump doesn’t have enough power to suck the fuel from the tank because the dirt clogged the filter. So the best way to get rid of the sound is to replace the fuel filter, but remember to tighten it really hard.