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No. What about: "All guests are here for the festival. Nobody is going to check out before that."
Your "infinite guests" -> "infinite different itineraries, including one where somebody checks out right this second" is the same wronh assumption as the "infinite universes"->"there must exists a universe where x....".
Just because there are infinite rational numbers between 1 and 2, does not mean any of them is 3.
You can have infinite guests and nobody checking out for an infinite amount if time.