To me it's not so much that the Nazis could have possibly won, but that they would have managed to pull of an invasion of mainland US and made it part of their empire.
Nukes. That's literally all. The premise is that Germany got nukes faster--the rest follows from that. They knew how to make them, but didn't have an Oak-ridge-equivalent town to convert into a giant particle accelerator to enrich the uranium. It could easily have happened had they invented centrifugal enrichment and hid the facility and the program well enough to not appear an appealing target. Using better encryption would have helped them.
If Germany got British and European opposition to either surrender, or crippled with a few well-chosen leveled cities, its chemical weapon, jet, and rocket programs would not have been stalled, and it would have had access to allied resources, fuel, etc. With no functional allies left, the US would have been on borrowed time. in the show, we know the Nazis took out DC, but we don't know if it was a sneak attack. The scene with young Obergrueppenfuehrer suggests to me the DC nuke was a sneak attack, possibly a sub-launched nuke, possibly the first nuke ever... dropping the first one on the US would make as much sense as anywhere else, both to harm the US and to demonstrate the weapon to the world without destroying any valuable real-estate and materiel in Europe/England. Remember that before the US had nukes, the Japanese were keeping it quite busy with a conventional war of attrition in the Pacific which historians agree would have gone on for years, even with the European Axis powers worn down to manageability.
It is a strength of the show that it doesn't elaborate on what happened, and leaves us to speculate. The younger characters in the show only know propoganda and censored history, which is scary itself.
