All players will have to start with the default regent - period.
The best way to get a regent of your own design into power is talk to the DM. If you come up with a good character and an interesting concept, we'll allow you to introduce the person as able assistance, and then you can groom him for taking over the reins of power later on.
If you can't cope with this, and MUST have your own super-regent to play, don't apply for a domain!!!