The invention of nuclear weapons seems like the overwhelmingly best case study.

1. New threat/power comes from fundamental new scientific insight.
2. Existential risks (nuclear winter, run-away nitrogen fusion in atmosphere).
3. Massive potential effects, both positive and negative (nuclear power for everything, medical treatments, dam building and other manipulation of Earth's crust, space exploration, elimination of war, nuclear war, increased asymmetric warfare, reactor meltdowns, increased stability of dictatorships). Some were realized.
4. Very large first-mover advantage with times scales of less than a year.
5. Feasible development in secret.

Nuclear weapons differed in that the world was already at war when they were developed, so policy makers would be in a different mindset and have different incentives. But otherwise, I think the parallels are as good as you could possibly hope for. The only other competitor is the (overly broad) case of molecular nano-tech, but this hasn't actually happened yet so you don't have much to go on. In contrast, the Manhattan Project is extensively documented.