There’s all kinds of ideas out there. From magnetic guns, to launch loops, to skyhooks. Remember we put things in the air all the time that don’t propellant, now many of them do use propellers, and that becomes a non-starter when you run out of air. And electromagnetic is very much propulsion, though not thrust.
There’s a lot of tech talk out there about how our love of rockets has held us back. Rockets actually kind of suck. But we understand them.
On the ground, you can push against the ground to move (e.g. automobile tires). In the water you can push against the water to move (e.g. speedboat). In the air you can push against the air to move (e.g. airplane).
But in a vacuum (e.g. space), there is nothing to push against. You have to carry everything with you, pusher and pushee.
That's why rockets are useful. It's not just that we understand them -- they work in a vacuum. If you're talking about propulsion that "overcomes Earth's gravity", it has to work in space, otherwise you're just re-inventing the car, boat, or airplane.
Not a physicist but Im pretty sure thats not true, they blow.