Humanitarian Purpose for your application?>
No agency is bound to consider any form of urgency unless it is truly a humanitarian issue or completely in the undeniable interest of the country you are applying to. Missing a booked flight is not truly humanitarian. It is not even their problem. Getting to a once in a lifetime urgent cancer treatment appointment is likely. Getting back because your direct family member is in hospital on terminal life support is likely.
If you meet the criteria for humanitarian consideration, check with their website how to apply. Again, be factual. Specific. Honest and keep it to point.