Can you finish a job without starting it?
If the job has pickup &amp; drop off locations, you need to visit the two locations in the correct order to finish the job. If the job only has a target location, then you only need to go to one location for completion.

From the official FAQ on page 5:


  Question: I don’t get doing Jobs: how do I do them? 
  
  ..... Each Job will have either a Target or Pick-up
  Location on the card. You then need to use a
  Move Action to get your Firefly to the correct
  location ..... Once you’re at that
  Location, use a Work Action to progress the Job.
  
  ..... If the Job also has a Drop-Off Location,
  you’ll need to Fly again to the Drop-Off Location
  to deliver the Goods before completing the Job. If
  the Job only has a Target Location, you’re done.


Note the use of the word "need" - it never says that the pickup location is optional.

Think of it this way - if you told someone you'll give them $10 to pick you up a burger from your favourite burger joint, and they give you a burger they already had in their car from somewhere else, they haven't really done the job you were paying them to do.