Do a test even if it seems that it is nonsense.
If the car is manual, try to start it by pulling it downhill and depending on how it reacts I can indicate more rightly.
Anyway, it should be checked on and injection, it will not be that the switchboard does not reach a positive start signal.
To start cold, the switchboard injects a very high amount of gasoline while the starter is turning it, once you release the key, that injection ceases and enters the speed of idle.
If the car does not start by shooting it, it is possible that the failure is that, and to check it, the engine cables will have to be checked.
A question, have you ever managed to start cold, keeps slowing down or tends to stop?