2007 TrailBlazer rough idle when cold

My 2007 TrailBlazer with 84K stumbles for 25 seconds
when I start up cold. After 25 seconds I hear a click and
then it runs perfect. Drivin me nuts. No engine codes present.
Have new plugs, new O2 sensor, new thermostat.
Any ideas would be greatly appreciated.

You may have no codes but a full scan looking at all inputs, pending codes and misfire counts may pinpoint the issue.

MaxWedge,
Thank you for your reply. I need to have it scanned.

Doing more diagnostics. Found out my TrailBlazer has a secondary air pump that pumps air into the exhaust manifold thru a control valve mounted on side of the head. On cold start up the pump pushes air into the exhaust manifold for 30 seconds to help 02 sensors warmup more quickly. I pulled off the hose on the air control valve on cold start and it pushes a lot of air for 30 seconds. If I unplug the control valve the engine starts good but has a check engine light on. Don't know if this is normal or not to have the engine run rough for 30 seconds on cold start up. Anyone else have a similar experience?

That is not the function of the air system,the o2sensors have their heaters built in. Possible the check valve is corroded and stuck.

I tried 2 check valves with the same problem.