Your first problem is just achieving critical mass. It doesn't matter what your dominant behavior or behaviors is. This is a combination of:
- Your community's scope - audience and subject matter
- Your audience's awareness of your community
- Having enough relevant content about your subject matter
Assuming you've chosen #1 to be a sufficiently wide audience and interesting enough subject matter, then you focus on #2 & #3.
In other words, you need to advertise as much as you can, and prime the pump with enough questions and answers until you have enough users to start reliably creating enough user-generated content.
One way to start is to recruit a cadre of subject matter experts who are in fact trying to solve problems in your topic area. I don't know how StackOver flow initially achieved this, but if they worked with 25 very good developers solving problems, they could have these people pre-recruited to ask and answer such questions.
You can take some cue by how StackExchange starts new communities in Area 51:
- Define & ask example questions - pre-build a list of content
- Recruit a cadre of subject matter experts who commit to the site
- Run the site among the early recruits to generate enough content before going live
Finally - you can shortcut this problem by engaging existing communities. In open source software, two well known tool-specific communities already pull from StackExchange tags to do exactly this:
Spring Java Community: http://spring.io/questions
Apache Cassandra project: http://planetcassandra.org/stackoverflow/
This lets you you leverage existing content, and drive awareness of your community among the population and encourage them to engage in your community in other ways besides Q&A.