Simply put, start with a niche market concept that helps solve very specific problems that people may have (such as delivering pet medicine to old or handicap people who live in villages or the countryside), and then to actually get started make an offer to those providing the solutions (the drivers) that is too good for them to refuse.

In this case I think you'd basically have to pay the drivers to make deliveries for yourself, and then work to show the value of this service to those whom need this service and are in a position to take over paying for it.