As others have said, get used to flying nights. Once you've got enough experience under your belt, your first flying jobs would probably be with a UPS/FedEx feeder carrier like Wiggins or Mountain Air, or some other night freight operator... there are dozens, many of them are small local operators. A buddy of mine got his start flying DC-3's for a local guy before getting hired on at TransStates.

UPS/FedEx are tough to get on with... you'll probably need airline or military experience first, and even then I'd recommend making a few friends who work for those companies. Internal recommendations are really helpful. Not so sure about DHL because much of their flying is contracted.

Good luck!