There are two intelligent species. One is far more technological advanced than the other, and could make contact at any time. However, it will wait until a specified condition is met, and only then initiate communications.
If the other species figures out it too soon, expect much anguish and attempts to cover up by the more powerful species.
Humanity can be on either side of the equation.
Contrast First Contact Math
- In Jack Campbell's The Lost Fleet series, they meet a species they end up calling the Dancers, which clearly have been monitoring humanity for some time. Once the fleet meets them in another system, however, they communicate and send back ships to human space.
- In John C. Wright's Count to A Trillion, the alien artifact about an antimatter star proves to be a trap: it was set up to alert aliens to the existence of an intelligent race that had developed far enough to be worth enslaving.
- In Star Trek, you have to achieve space flight on your own. In theory.
- Stargate SG-1: The Asgard, a race of benevolent Greys who masquerade as the Norse pantheon, include tests in their holy sites to determine when the Transplanted Humans inhabiting worlds they control are ready to see them as they really are. The site on Cimmeria, for example, has a test of selflessness followed by a test to see if you have basic geometry skills.