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?