The "infinitely long" ladder in question can be understood as "long enough" to be strong and undeformed even if it is millions of kilometers long. Before exploring this hypothesis, we need to focus on the core of this thought experiment, without considering issues such as materials, processes, fixations, and the supply of materials to the earth. Let's start with some knowledge related to the first cosmic velocity.

Objects on Earth are fixed to the surface of the Earth under the influence of the Earth's gravitational pull. To leave the Earth's surface, this gravitational pull needs to be overcome, and there are usually two ways: one is to continuously apply upward momentum to keep objects or people away from the Earth's gravitational range, such as the principle applied during the liftoff phase of a rocket, or to convert one's chemical energy into motivation to climb by climbing a ladder.

The method in the question belongs to this approach, and we will make a comprehensive analysis of its feasibility later. The second method involves changing the direction of the object's motion so that the direction of motion is angled to the direction of gravity, so that the object is prevented from being pulled directly back to the ground by gravity, which is a circular motion. Before this motion can be realized, the object needs to have a sufficient initial velocity, which is known as the first cosmic velocity.

The first cosmic velocity is defined as the velocity at which an object moves in a uniform circular motion around the Earth near the ground, also known as orbital velocity. This calculation can be found from the relationship between gravity and centripetal force and gives it to be 5.0 km/s. Reaching this speed allows for orbiting the Earth's surface, but does not mean that it completely escapes the Earth's gravitational pull. It is important to note that the orbital velocity decreases with altitude, e.g. to 0.0 km/s at twice the Earth's radius and 0.0 km/s at ten times the Earth's radius.

If you combine these two ways, if the ladder is long enough, it can become part of the earth and rotate with it. Since the ladder rotates at the same angular velocity as the Earth, the linear velocity at the top of the ladder increases with height. Assuming that the orbital velocity of that altitude is reached at a certain altitude, the person leaving the ladder from here will become an artificial satellite orbiting the Earth, orbiting without reaching the first cosmic velocity.

For the realization of this phenomenon, the orbital altitude is geosynchronous orbit - about 1 km. At this altitude, the linear velocity at the top of the ladder is 0.0 km/s, at which a person can not fall back to the surface while orbiting the Earth, albeit at a speed lower than the first cosmic velocity.

However, going beyond 36000 km will produce a faster linear speed, increasing the centrifugal tendency of the portion above this altitude, resulting in the possibility of the ladder being destroyed, or having a fatal effect on the planet. If the theory of gravitational overcoming is valid, and a complete circumference of the Earth is considered "leaving the Earth", the answer is yes: you can leave the Earth if you have climbed to this height and have not reached the first cosmic velocity.

如果思考物理意義上完全離開地球引力，即引出“希爾球”概念，為尺度以內完全受行星引力主導的區域。對於地球，此球半徑約為150萬公里。理想化情況下，梯子需達此高度，但此速度遠超第一宇宙速度，因此答案在此假設下是否定的。

In conclusion, if one thinks that orbiting means leaving the earth, the answer is yes; If it is required to get out of the gravitational circle, it is denied; If you need to reach an escape velocity to leave, the answer is also yes, but be aware of the above risks.