Cold start and running problems

Hello,

I have the car listed above RWD. I've had a problem since the end of 2018 that isn't getting diagnosed; in the morning upon cold start when I drive if I press the gas pedal half way down the power cuts off and then comes back on again and it starts running this happens for the first five to seven minutes of drive every time I let go of gas pedal and then press it half way down I starts doing it again but after five to seven minutes of running the car becomes normal and is not as bad for the rest of the day running but after leaving it parked for about four to five hours the problem reappears but not as bad as it's in the morning cold start. I've even changed the fuel pumps plus throttle body, fuel pump relay in fuse box but still the problem persists and I've run out of options there is no check engine light and the guy working on my car says he took it to several diagnostic scanner places where they did live scan and looked for stored codes but they didn’t find anything

I’m beginning to suspect intake air temperature sensor I cleaned it but no difference can buying a new IAT sensor fix my problem?

I'll appreciate any help about my car's problem, I’m in a though financial spot.

Thank you