Sounds like the same issue I've got, different car but the basic's are the same - Intake Air Control Valve, if this little unit is giving problems either with faulty motor or just dirty seals, then you'll get this issue, it helps maintain and controls the idle feature
On mine, ... when I start the car without any acc, the car starts then just dies, no hunting or splutting, just lose revs and stalls, nothing I do will stop this. If I start the car with acc, the car revs and then sits perfect at the correct idle and stays there.
The problem is not so evident when the car is hot, not warm but hot so if you switch off and start within 10 - 20 minutes, no issues, leave it longer and the problem returns
Hope this helps in your quest to find the problem
BR
Paul