There are several pre conditions and self tests conducted just before start, right after start, and between 0 and 5 mph
You may or may not hear all of them...
As state above, there is the air pre charge to the exhaust catalyst
There is the Anti lock brake (ABS) system test that should cycle the brake pump and depending on the result it may do it again during initial roll.... if good then no light. This one usually is not loud enough to hear, but you might feel rapid pulses in the brake pedal for 1 to 3 seconds
Not a test or pre condition.... the Air Conditioner / Heater controls are vacuum actuated.. there is a vacuum reservoir that may loose it's vacuum overnight (usually in colder weather). In the hot cold and vents control system is a "Blend" door that will fall open if the vacuum is lost... On engine start, the reservoir's vacuum increases very fast and the "blend" door can slam shut making a startling noise.... if this happens at every motor start cycle, then you should have the AC / heater control system checked for vacuum leak(s)
The fuel tank is directly below driver and passengers seats and there is a electric pump inside it... if the fuel pressure in the injector rails leaked down after last stop, then on key to "run", or power on..the pump will cycle until pressure is up.. if the car motor is not running, you may or may not hear this normal activity
Under the dash is the Service Accessory Module (SAM) sometimes called a General Electronics Module (GEM) these usually have several small relays inside. As various systems are energized, you may or may not hear the normal relay clatter