How do you know you can do that, though?

The player is basically Talos manifest in flesh. That's why the game is so compelling in the first place: you think you don't want to align with the Imperials because they tried to kill you. You really don't want to align with the Imperials because they banned worship of you. The Stormcloaks support Talos worship, but they're dogshit otherwise, though I would argue that Ulfric Stormcloak is the rightful High King of Skyrim. The Stormcloaks are ultimately right, but they're just shit people. If they weren't racist, if we got that entirely out of their culture, if Windhelm was a melting-pot of Nordic and Dunmer culture, the choice would be easy, but then it wouldn't be such a heavy choice to make that we do not have a clear consensus 15 years later. (Shit, I just realised today is 15 years to the day since it released, 11-11-11, which is accurate no matter how you write the date (for me, 2011-Nov-11).)

If that doesn't change your mind, consider the urchin added by Hearthfire who lives in Windhelm is based on Aerith from Final Fantasy VII. Tell me she isn't. Red dress. Sells flowers. Dad was killed in the war. (Okay, we don't know who Aerith's dad was. It was the husband of the woman who took her in, who was killed in the war. Close enough!)

So yeah, Talos reincarnated theory. Never proven, but it does explain how we can know everything for a second playthrough.

Note that Starfield actually does address this with its NG+ mode. You can't really explain the divine knowledge in Fallout 4 (or any other Fallout), but Elder Scrolls games have the Talos/Akatosh reincarnated theory, and Starfield has its NG+ directly address the situation.