TL;DR: Release your app as pre-order ASAP. Get hundreds of new users shortly after releasing it.
I've made my app Pompom (getpompom.com) available as a pre-order on the Mac App Store a few weeks before it launched. What it does is that the app is visible in the App Store and people occasionally came across it when searching for apps. They can click "Pre-order" and get notified when the app is launched.
My app wasn't ready to launch at that stage but you can update the app before it's released and you can change release date multiple times. So there's no risk involved in making it available as a pre-order.
The result?
When I launched the app, I got 118 new users within the first two days, and about 270 in a week - without doing any of the marketing.