It's a mass problem. Instead of imagining the gravity well as something moving away from earth out into the vacuum of space, think of it as a ball that needs to be rolled uphill - even if you give it a huge burst of energy, it's not going to go as far as you think from that one big push, and it's still going to roll back downhill. In order to make it out of the gravity well, you need a lot of focused, continuous energy over huge distances.
There are other factors, too - imagine you're trying to send a penny around the entire equator of the earth, and think of the largest possible explosion you could subject it to without vaporizing it. A stick of dynamite could launch a penny only around a half mile's distance around the equator, assuming ideal conditions, which is about .0025% of the circumference of the earth, which is 10% of the distance between the earth and the moon, and the moon is about 25% of the distance from which earth's gravity stops being a significant factor.
If you carefully deployed a large number of well timed series of dynamite sticks precisely located so that each blew up perfectly beneath the penny at its apex following each previous explosion - you'd need 150-300 sticks to get the penny out past the edge of the effective gravitational well, the point at which other factors in the solar system have the dominant influence - it'd effectively leave earth and start falling toward the sun. At any point closer to earth than that, it will slowly and inexorably return back to earth, reaching up to 25,000 mph before vaporizing itself in the atmosphere (if it fell from the outer edge). If you had no atmosphere, a clear shot, and the "ideal" penny cannon to launch it, you could hypothetically reach escape velocity with only a quarter stick of dynamite.
Incidental bursts of gas, or even outright exploding objects in space are not going to launch a bunch of stuff into much deeper orbit. There's a constant downward pull, and gas and dust creating drag and downward acceleration the closer in you get, and just vast, incomprehensible distances to travel under the influences of gravity. Getting things to go faster than 25,000mph, or reaching escape velocity, without vaporizing the thing you're trying to make go fast, requires as big a continuous explosion as you can make over as long a time period as possible.
I love that AI can whip up an xkcd style "What-If?" type scenario for these questions.