... we put a fire station pole between the earth and the sun

First, let's get a few things out of the way:

In real life, we can't put a metal pole between the Earth and the Moon. The end of the pole near the Moon would be pulled toward the Moon by the Moon's gravity, and the rest of it would be pulled back down to the Earth by the Earth's gravity. The pole would be torn in half.

Also the Earth's surface spins faster than the Moon goes around, so the end that dangled down to the Earth would break off if you tried to connect it to the ground.

There's one more problem:The Moon doesn't always stay the same distance from Earth. Its orbit takes it closer and farther away. It's not a big difference,  but it's enough that the bottom 50,000 km of your fire station pole would be squished against the Earth once a month.

But let's ignore those problems! What if we had a magical pole that dangled from the Moon down to just above the Earth's surface, expanding and contracting so it never quite touched the ground? How long would it take to slide down from the Moon?

If you stood next to the end of the pole on the Moon, a problem would become clear right away: You have to slide up the pole, and that's not how sliding works.

Instead of sliding, you'll have to climb.

People can climb poles pretty fast. World-record pole climbers can climb at over a meter per second. On the Moon, gravity is much weaker, so it will probably be easier to climb. On the other hand, you'll have to wear a spacesuit, so that will probably slow you down a little.

If you climb up the pole far enough, Earth's gravity will take over and start pulling you down. When you're hanging onto the pole, there are three forces pulling on you: The Earth's gravity pulling you toward Earth, the Moon's gravity pulling you away from Earth, and centrifugal force from the swinging pole pulling you away from Earth. At first, the combination of the Moon's gravity and centrifugal force are stronger, pulling you toward the Moon, but as you get closer to the Earth, Earth's gravity takes over. The Earth is pretty big, so you reach this point while you're still pretty close to the Moon.

Unfortunately for you, space is big, so "pretty close" is still a long way. Even if you climb at better-than-world-record speed, it will still take you several years to get to the crossover point.

As you approach this point, you'll start to be able to switch from climbing to pushing-and-gliding.

After another few weeks of gliding along the pole, you'll start to feel gravity take over, speeding you up. When this happens, be careful—soon, you'll need to start worrying about going too fast.

As you approach the Earth and the pull of its gravity increases, you'll start to speed up quite a bit. Since you have this handy metal pole, you can control your descent by clamping onto it and controlling your rate of descent through friction.

Assuming you descend slowly and enter the atmosphere in a controlled manner, you'll soon encounter your next problem: You're about to drop into some extremely strong winds, so you should wear lots of protective gear. Make sure you're tightly attached to the pole, since the wind and various shockwaves will be violently battering and jolting you around.

At some point, to reach the ground, you're going to have to let go of the pole. For obvious reasons, you don't want to jump directly onto the ground. Instead, you should probably wait until you're somewhere, where the air is still thin, so it's not pulling at you too hard—and let go of the pole. Then, as the air carries you away and you fall toward the Earth, you can open your parachute.

Then, at last, you can drift safely to the ground, having traveled from the Moon to the Earth completely under your own muscle power.