They might recalculate the "time of the end".
If they accept 587 BCE for the fall of Jerusalem (instead of 607) and take 365 days per year (instead of 360), they come to 1969.
They can say that Satan used the moon landing (instead of World War I) to distract people from God's Kingdom.
First, they can say that "the generation of 1969" will not pass until the end comes. In 2049, they might change it so that the "generation" is the "evil and adulterous generation" that is on earth since 1969.
Some years later, they might teach that the anointed are the "generation".