Hey guys,
Above is a video I shot yesterday of my car starting up. It's been doing this for a little while and I am ordering some other parts today and would like to get it fixed, it's annoying.

Things to look for in the video:
0:00 - Car starts and you can immediately hear a deep, throaty growl that sounds like it's coming from the passenger side of the engine compartment, underneath the MAF sensor area. RPM is at 1,100

0:57 - Deep throaty rumble noise ceases and car quiets down. RPM at 1,100

1:21 - Car quiets down significantly to normal level and RPM's drop to normal level at 800

I have tried to diagnose this before and people told me it was the SAI pump. But it doesn't have that "Jet Engine" sound, it's more of a growling. The issue occurs every time the car has been sitting for an extended period of time i.e. in the morning, and after work.

Car:
2004 B6 A4 Cabriolet 1.8T
Intake filter: K&N
No Mods whatsoever

Any thoughts would be appreciated

Thanks!