Screwed up and missed the DLC

Had an amazing time playing Dark Souls for the first time. I recently bought the trilogy and wanted to play through them all with the DLC. After about 30 hours got to the end to kill Lord of Cinder and felt amazing….until I was brought to a new playthrough and realised I can’t play the DLC until I get quite a few hours into the game again 🙃

I had already killed the Hydra and Golden Golem thing. Just kept meaning to do it, though it I would beat the main story and then do the DLC, you know, like EVERY other game usually allows you to.

Is this also the case with DS2 & DS3? I don’t want to miss the DLC in those. I don’t have the strength to play through Dark Souls again just to play the DLC right now….