Hello,
It sounds like you might have a faulty crankshaft position sensor.
The crank sensor can fault out with temperature. Typically when the engine is hot/warm the crank sensor will have starting issues.
The reason the vehicle runs rough for a little bit after you start is that is the time when the excess fuel gets burnt. As during the cranking over and not starting the injectors are still spraying fuel to the cylinders and you will have more fuel than its required.
You might find these articles helpful:
https://www.2carpros.com/articles/how-a-crank-shaft-angle-sensor-works
https://www.2carpros.com/articles/symptoms-of-a-bad-crankshaft-sensor
https://www.2carpros.com/articles/crankshaft-angle-sensor-replacement
I have attached the diagrams for your reference.
Please let me know of any questions.
Thank you.
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Tuesday, August 10th, 2021 AT 8:02 PM