Assuming one could create a staircase and walk to the moon, would escape velocity still be a factor in leaving the Earth's gravitational pull? I'm not a physicist but am just curious to know.
A space elevator has been proposed. With currently available technology it would be very expensive to build one, but not necessarily impossible.
Assuming the staircase or elevator being fixed at some point on Earth near the equator, the Earth's gravitational pull is compensated by centrifugal force at a height of about 36,000 km, in the geostationary orbit.
That's the height you would have to climb to, before you could slide "down" to the Moon along an even more expensive construction stepwise adjusting your velocity to that of the Moon. The total trip would be at least about 400,000 km, that's ten times around the Earth.
Your weight would decrease, the higher you climb from ground to the 36,000 km height. Assuming you make 3 km of height each day, it would take you about 34 years to reach geostationary orbit.
Then sliding down with 10 m/s would take at least one more year to reach the Moon. Hence, it's possible with a one-way trip of about 35 years, assumed the technical infrastructure is provided.
But it looks easier to take an appropriate vehicle.