Other than reviews, you should be paying attention to ASO (app store optimization). Search represents 80% of organic downloads on Google Play. This is pretty basic stuff if you're familiar at all with Google SEO. Focus on Keywords.
-Put your main keyword in your app title (can affect position 80-100 spots)
-Use your keyword 5 times in your app description (unlike the App Store where the app description is not searchable) (can affect position 10-20 spots)
-Google play searches also rank by downloads, which im guessing you don't have too many of since your app is new.
Also, make sure you have attractive screenshots, and take advantage of the opportunity to add a youtube promo video for your app
It is true that having people write review will have a big impact- the number of links to your Play Store page improves search rankings.
Here are some good Android review sites: AndroidTapp, AppBrain, AndroidLib, AndroidApps, AppsZoom. There are tons of them out there.