Most quests can be started at any level if you meet certain conditions. For example Tyranus will show up in Markarth if you are either level 20 OR the Hall of the Vigilant has been destroyed. You can start The Only Cure early by being diseased. PotP will start early if you’re a murderer since Silus has use for someone who isn’t afraid to sully their hands. Barbas is willing to seek out even a weak Dragonborn to help him. A hunter of vampires may beseech Meridia for aid.
Dragonborn only forcibly starts after Sky Haven Temple has been completed. You can still begin by traveling to Solstheim and visiting Miraak’s temple, but I wanted to reduce the narrative demand to deal with Solstheim so early on if you wanted to be able to fight random dragon spawns. It’s also nice to not have three expert-destruction cultists knocking on your door when you’re still weak.