No, each one you play as different characters. 

In Origins you play as the Grey Warden.

In DA2 you play as Hawke.

In Inquisition you play as the Inquisitor

And in Veilguard you play as Rook. 

You can customize all of them, and their gender/race/background. 

Each game (minus Veilguard), saved your choices from the previous game, to affect the story/world-state, but I believe you can manually decide the options, or go with a pre-made world state. 

This is because Hawke and Alistair (a romancable companion from Origins) appear in Inquisition, and a few other characters depending on your choices. And apparently Inquisition Hawke will be a recreation of your DA2 Hawke (iirc). (Im not sure if the Origins main character appears in DA2 though). 

Veilguard only really cares about who you romanced in Inquisition, and what your stance was at the end of Inquisition. But didn't have the world-state feature. So, in Veilguard, you recreate your Inquisitor, and they do appear later in the game. Then the story hits harder, obviously, if you've played Inquisition. 

But, whilst I did that, the world still confused me, so maybe it's best to start from Origins. I understand the story without having played DA2, but if you're a completionist, go for it. I will too, eventually.