Have you had it checked for codes to see if any are present?
As asked already, does it try to crank over?
When you first turn the key when it is cold, do you hear the pump priming sound?
If it does it every time it is cold, are you able to test the fuel pressure while it is cold?
If the fuel pressure is fine, and the car cranks over fine, I'd try to spay some carb cleaner into the intake and see if it fire up right away when cold when you do this.
If so it is a fuel delivery problem, and we can go from there.
Another thing to check when it won't start is spark.
Here is a thing to read to help you learn how to do this.