You could have an eccentric orbit that swings far out into the solar system and then when it approaches the sun again accelerates to reach the escape velocity of the sun. But that would take years.

And I think still only be rather slow once it escapes the solar system since the escape velocity would be almost used up.

There is the concept of a nuclear photonic rocket - Wikipedia which I think of as a light sail and a white hot glowing lump of nuclear fuel on a string.