@VoxSomniator Earth's orbital speed is about 30 km/s. To fall into the sun, you need to cancel that out by having a rocket with 30 km/s of Δv. On the other hand, escape velocity from the solar system, which is what you need to exit the solar system on an essentially arbitrary path, arbitrary enough to get to anything within the plane of the galaxy pretty easily, is only about 40 km/s, so you can take that 30 km/s you already have and you only need 10 km/s more.
@VoxSomniator well there really isn't a fast way.