Now there are multiple private teams who could actually pull it off. Or maybe not... I have no idea how hard it would be to make a signal source appear from Earth as if it came from a fixed star, but I suspect it would be extremely difficult to accomplish for any length of time. It's not as if you could just park it someplace. Then there's parallax to consider.
In any event, the message wouldn't be "Build a spaceship with technology no one has ever seen before." The message would be "Get your act together or we'll bulldoze your planet to make room for a hyperspace bypass," or "Take the red pill LOL" or "Get Amazon Prime today. The bargains are out of this world!"
The Iraq war?
It's a bit much to start an entire deductive reasoning based on such a blatant assumption.