newtonian mechanics - Can we escape Earth's gravity slowly?

I had a recent conversation with my girlfriend, who is a physics grad student. She was kind enough to listen to me rant about an idea concerning escape velocity. Unfortunately, I am still thinking about this question, but don't want to bother her with it.

My thought is that we shouldn't actually need to reach 11km/sec to leave the earth's gravity. Instead of this, can we simply apply enough force to overcome earth's gravity without reaching that speed? How we would do this is not a part of my question.

Orbital altitude is $99$ miles. Travelling $60$ mph straight up should get you there in $1.65$ hours, granted you have enough force to push. I know some of the simpler math like $F=ma$, but that didn't help me understand.

I browsed some articles about space elevators and couldn't find my answer.

Then I thought about a regular elevator and the fact that it has enough force to move it away from the earth successfully. Even if the elevator moved at $1$ nanometer/sec, it would still move away from the Earth, overcoming the minute pull of gravity at that altitude.

If you missed it, my question was: can we simply apply enough force to overcome Earth's gravity without reaching that speed?

Edit: In another example, let's say we could drive a car from here to low Earth orbit. As long as we had enough torque, we should be able to overcome gravity, much like a pickup truck pulling a bunch of lumber. Is that correct?

Answer

Escape velocity is how fast an object must be moving to escape another object's gravity without needing any additional force/acceleration. The examples you've proposed are perfectly valid ways for objects to escape earth's gravity without attaining escape velocity but only work because some kind of force is continually pushing/pulling the object ever upwards. So in short, yes, if we had enough torque, and an engine that had enough fuel to run long enough to reach the desired altitude, then escape velocity need never be attained.

I believe what you are trying to get at specifically is whether an object moving at constant speed could escape the earth's gravity. The answer is yes, as long as you had a force to counteract gravity and allow the object to continue to move upwards.