I don’t really keep these facts at the forefront of my memory believe it or not but the Saturn V was one big c**t of a rocket with about a million gallons of fuel.
That’s unimaginable. Couple that with accelerating through less and less dense atmosphere it’s really not that unbelievable. Get rid of the air resistance and it’s just not a big deal with just gravity to fight, which is a steady and consistent force, unlike the turbulence due to air.
Even at an acceleration of 3 g, which isn’t outrageous, you’d get to 25k mph in 22 mins (I think).