The first route is at the Kiln of the First Flame bonfire, where a second bonfire will appear that will transport you to first area in the DLC called the Dreg Heap (the bonfire is next to the Soul of Cinder, the final boss of the game.) There is no need to complete the game to get the DLC. So consider yourself warned if your level falls behind the recommended one. The DLC is a late-game content, meaning you must be at least level 125 or higher to get there. Just a caveat: accessing the DLC depends on how far you have gotten to the main game. In The Ringed City, you must interact with a bonfire. In Ashes of Ariandel, the player needed to talk to an NPC to get to the DLC. The developers wanted to make the DLC as thematic and organic. Unlike most games, getting a DLC in Dark Souls 3 isn't as simple as getting a prompt.
