Idles high when first cranked and then drops to a rough idle.

Get a can of throttle body cleaner and remove throttle body and totally clean it. Remove Idle air control valve, tear it down and clean it also. Or buy a new IAC. Clean MAF with special cleaner also. Can buy both at any auto store.

Check the resistance across the IAT sensor. Inlet air temp sensor. It should be around 30,000 ohms. Mine showed no resistance(open) but if I softly moved the sensor element it would work and show resistance. This will shake and open up under normal driving conditions and give the engine no temp signal which would give you a rich fuel mixture. Good luck.

I have had this issue for about 3 years and I finally figured it out! Same issue as you first time startup goes to 2000 RPM then when it drops it has a very rough idle even drops below 200 RPM almost stalling.It ended up being a DPFE sensor I got the part from RockAuto for $50, keep in mind the check engine light was on. If your check engine light isn't on I'm going to guess that there is carbon buildup in the EGR so just clean the passageways through the throttle body. I hope this will help you if you are still having an issue. Thanks