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[Game of Thrones] The Night King never obtains a dragon. What's his backup plan for getting past the wall?

In this scenario, Daenerys never goes past the wall and Viserion never gets speared and reanimated. Either the ranging to capture a wight goes as planned or the idea is never considered. With that in mind, did the Night King have a second more time consuming plan or did everything hinge on having a dragon to breach the wall?
gpt
The undead Benjen Stark refuses to approach the wall too closely, remarking that it's more than ice - it has spells etched into its foundations.  These are likely the same spells that were originally used to protect the Three-Eyed Raven's cave, which caused wights to de-animate and fall apart when they attempted to cross its threshold.

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That ward was broken when Bran Stark - already behind it - was marked by the Night's King while using the greensight, allowing both Others and their wights to enter it.  Bran may well have broken the ward on the wall, too, when he crossed back towards Winterfell.  If that was the case, his forces could have simply climbed over it.  If living Free Folk can manage it, a tireless undead army should be able to as well.

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If that *wasn't* the case, he'd need to either find and mark Bran (or another greenseer) again, or wait for an opportunity to present itself.  This is likely what he's been doing in the time since the Long Night - an ageless being can afford to be very patient.