This is very confused. To leave the Earth’s gravitational grip you need to impart a certain minimum change in velocity. You can do this all at once or or we time but it doesn’t matter. The delta-V is the same.
To give an example, if you provided propulsion to move an object at 1 mile per hour, you could turn off all propulsion and the object would have escaped Earth's gravity once it was 4 * 10^12 km away. This is, of course, an extraordinary waste and probably practically impossible.
I provided a very specific computational counter-example to your statement. You’ll need to start there if you wish to compose a serious reply.
I’ll restate the counter-example for your convenience. One can provide just enough continuous thrust to move an object at a fixed unchanging speed of 1mph for a long time (about 283 million years), at which point it will have reached a distance where the escape velocity is only 1mph. Once it has surpassed that distance, one can disable the thrust and the object will have completely escaped Earth’s gravity without ever having moved at more than 1mph. It will then asymptotically slow down to 0 mph over an infinite amount of time.
There is ample introductory material on Newtonian physics that you could learn from, only a google search away. It’s disrespectful of my time to assume I must be on the hook to handhold you through it.
Imagine that I have a spacecraft with imaginable engine which is able to indefinitely provide thrust enough for this spacecraft to move straight up from the planet’s surface at the constant speed of 1 mph.
Will this spacecraft leave the planet in indefinite amount of time or not? If not - what is going to stop it?
https://www.quora.com/Escape-velocity-is-supposed-to-be-24-0...
Multiple answers explain that there isn't a fixed minimum change in velocity required for an object to escape Earth's gravity.
https://www.quora.com/Does-rocket-always-need-the-escape-spe...
The first answer here explains the same thing, using basically the same example (1 m/s instead of 1 mph).
https://space.stackexchange.com/questions/4688/couldnt-i-esc...
The answers here overwhelmingly reiterate and support the same example in this thread.
For instance, if you had a rocket with a fixed delta-V and it used all of its energy almost instantaneously, say it escapes from Earth. But if you lower its thrust so that it is not accelerating upward (lower than the force of gravity), it could use the same delta-V without leaving the ground.