Life itself could arguably be a Von Neumann probe. It's so good at spreading that it's a problem, when we send probes to other bodies in our own solar system we often sanitize them because we worry life will hitch a ride and start colonizing.

Life on a planet is a lot like a continuous fire, fires often send out embers that start new fires elsewhere.

You send out little packets of life to new places, wait single-digit billions of years (a blink of an eye for the universe, really), boom: new intelligent species with potential to shoot more seeds out into the universe.