okay i apologize for letting this topic off the rails by mentioning a reactionless thruster.
keeping it real and in the twenty-first century,
colossal carbon tubes have the specific strength needed for a space elevator.
if a climber could accelerate as it goes up, then at a modest 1.1g it would reach high subsonic speeds in five minutes.. at which point it would be ~44 km out.
at 300 m/s top speed, total travel time from surface to 30,000 km out would be ~28 hours. but after reaching space, it could perhaps go faster?