[kibwen]

I'm not sure if it's actually impossible. IANA physicist, but if your singular all-consuming goal was to get out of the solar system as fast as possible you could probably get a better gravity assist from a single pass of the sun than Voyager got from the entire grand tour.

(Feel free to correct me, physicists!)

The bigger issue is convincing someone to hand you millions of dollars to literally throw away faster than anything in prior human history.

[jlgreco]

Well, technically most of the mission cost would be spend on Earth (paying Earth engineer salaries, and Earth factory bills), so the money never leaves Earth. The only money you are literally throwing is the material cost of the rocket and probe, which would be fairly low (the cost of a bunch of titanium (or whatever the rocket/probe is made of), silicon not worth measuring, the rocket fuel (which is surprisingly cheap), etc.

[ars]

> get a better gravity assist from a single pass of the sun

No. The gravity assist is because of the motion of the planets around the sun. The sun isn't moving relative to itself. There are some other things you can do where the sun can help, but not a slingshot.