Can you swap in a known-good Idle Air Control? The IAC would be my first suspect.

Its location is close enough to the block to get some warming as the engine heats up, and that may loosen up sticky residue inside it.

Older cars with carburetors and accelerator pumps benefit from pumping the gas pedal on a cold-morning start. With FI engines one runs the risk of having too much fuel from multiple start attempts, which must burn off after the engine starts. It can run rough from a too-rich mixture during that time.

If the check valve in the fuel line is failing, the fuel delivery system can lose pressure overnight. In that case it is necessary to turn the key on and off several times to pump up the fuel to the needed pressure.

Hope this helps.

Bob

:>)