There are some basic benchmarks on the number (and, more importantly, the quality) of questions needed to exit private beta. I'm not going to quote specific numbers because we just use them as loose guidelines anyway.
The big picture is that a private beta has to generate enough interesting content to avoid the Empty Restaurant Syndrome.
As the community's "founders," you need to prove that you have something interesting to talk about. You need to establish that your subject has good on-topic questions which receive solid answers. Additionally, you're supposed to establish an strong, active meta community brimming with discussions about what does and doesn't belong here.
If it turns out that the subject is more niche than we all expected, we may choose to extend a private beta past the first week. And if a new site fails to reach these basic benchmarks, it is possible that the site will not find its way to public beta.
But right now, just focus on asking great beta questions!
This post has been migrated from (A51.SE)