Its better to ask for sponsorship before you start a job. the extension although I am not fully aware of it can take effect if you have the required degree that are eligible. I am have known people whose extension has been approved on the basis of volunteer job as well so you might want to explore that option as well. Your Int'l advisor can give you a brief on that. You can also consult one of the lawyers. Remeber there are loop holes that can be explored

Peace