Tevinter is not just filled with magisters and slaves. There is the soporati class.
The protagonist could just start out as a soldier/mercenary or someone just living in some remote village who has never seen a city before.
Although, Tevinter does give the unique opportunity to starting as a household servant/slave to an Altus or powerful Laetan. Then the head of the house is killed in the open by a rival, and the servant/slave has to make it on his/her own afterwards. So, they may go that route. It's just not the only route.
I would like another origins-like beginning.
Mundane human - Laetan household guard or soldier/mercenary.
Mundane elf - slave, Laetan household guard, or city elf
dwarf - Laetan household guard or gladiator
elf/human mage - member of a Laetan household currently studying at a Circle.
Or whatever they can think of. It is just nice to get that background and establish the character. I wouldn't mind if they don't have fewer side quests compared to Inquisition if they used those resources to build up an Origins-like beginning again.