In a galaxy far, far way, and long, long ago, the first civilization known (to itself) advances past Level II on the Kardashev scale (yet is not to level III). They still have not found ANY evidence that life has evolved anywhere besides their planet.
Due to this, scientists are instructed by the head of their governments to create an equation that predicts every possible form of life. What they can be composed of (depending on the set of materials on the planet), and how to create them depending on those materials. Then they create automated space crafts, fill them with reprogrammed grey goo, and send the crafts across the universe to seed planets with life.
After 100 years, a cataclysmic event occurs, and destroys the species, but the spacecrafts go on to seed the universe with life so thoroughly, that modern-day aliens are left wondering "how could such a numerous and extreme diversity of life occur on nearly every planet?"
Is such a scenario feasible?