Assuming that your are not manipulating DA, my experience that sites can start ranking for terms with sufficient search volume around DA 35.
Now keep in mind if you buy a ton of junky links or redirect domains you can be DA 35 over night but that doesn’t mean you will rank, as the other posters have mentioned.
However, if you are doing legitimate non manipulative link building, then around DA 35 is when you can expect to start seeing some nice rankings.
My experience is with blogs, so if your not running a blog then your mileage may vary. Almost every blog I have run has seen a bit of an increase in rankings after certain milestones, such as 50 posts, 100 posts, 200th post, 1 year old, and 2 years old. (This is also supported by a bunch of information online)
So keep building natural links, and keep producing quality content and keep working towards the various milestones.