1. They're expecting their first child September 5.
2. They're expecting their first child on September 5.
Which of the above sentences is correct?
I'm not a teacher.
be expecting a child/ baby = be pregnant
So if you want to say that the child will be born on Sep 5 you can say:
They’re expecting their first child who will be born on September 5.
My opinion is a reference. Let’s see other person’s suggestions
The second sounds better to me.
I hardly need add that most babies decide for themselves when to emerge into the light, so a due date of 5th September is widely understood to mean early in September.
Rover