can start a sentence with, ' Not long after that?" Not long after that, the police came
Is it more to spoken?

Question

can start a sentence with, ' Not long after that?"  Not long after that, the police came
Is it more to spoken?

Answer

Of course, but you need to have a  sentence before that to explain the situation. 
 Example: I heard a scream from the flat next door.  Not long after that, the police came to investigate.

Answer

Yes.