Note that the Doomsday Argument (or better, the underlying self-sampling assumption) is actually a counterargument to very short timelines:
By definition, we have a 95% probability of being in the central 95% of the human civilization lifespan; that means a 95% probability of human civilization lasting at least 1⁄39 of its past duration (and at most 39 times the same duration).
Given that civilizations with biological humans around have existed since at least 10000 years, this would give 95% probability of human civilization lasting at least another ~250 years.
(based on an old argument by Richard Gott; obviously you can play with the numbers to obtain different results, but the basic intuition is that we probably have more than a few years left)
Note that the Doomsday Argument (or better, the underlying self-sampling assumption) is actually a counterargument to very short timelines:
By definition, we have a 95% probability of being in the central 95% of the human civilization lifespan; that means a 95% probability of human civilization lasting at least 1⁄39 of its past duration (and at most 39 times the same duration).
Given that civilizations with biological humans around have existed since at least 10000 years, this would give 95% probability of human civilization lasting at least another ~250 years.
(based on an old argument by Richard Gott; obviously you can play with the numbers to obtain different results, but the basic intuition is that we probably have more than a few years left)