Get your friends and family to download and give good android reviews, as the more downloads and good android ratings you have, the better your rank will be. Using forums like Quora and Reddit can also help. This requires a ton of creativity, as you can't just go around promoting your app with android app promotion. You'll probably get disqualified.
I just read a review from someone that complained how a few days after he ended his campaign (he put in a lot of money and got into the featured list) his app went way down the list again... Sometimes paying for ads is the way to go (especially if you think it'll spread organically after your campaign) but it's not always the way to go. It's very easy to spend all your cash on ads, but you have to have a very good plan on getting it back.
Build a social community on Facebook and Twitter. It takes time, but it's something you'll need to retain your community and keep them involved. You have to post good quality content and make them feel part of something. You should let users access your social pages through your app. People nowadays only click on things that are very "clickable" and in front of their faces.
Try to get reviewed onwebsites that do app reviews and on YouTube channels that do app reviews. Send them an email, or if you can't find it send them a message on social media. You can do both. Be persistent with them, and don't get discouraged if they don't answer you after the first or second time. They're like all of us - sometimes we pay attention to something only the fifth time we see it. Just make sure not to give them a feeling that you're spamming them (even though that's actually what you're doing.
Try to get reviewed onwebsites that do app reviews and on YouTube channels that do app reviews. Send them an email, or if you can't find it send them a message on social media. You can do both. Be persistent with them, and don't get discouraged if they don't answer you after the first or second time. They're like all of us - sometimes we pay attention to something only the fifth time we see it. Just make sure not to give them a feeling that you're spamming them (even though that's actually what you're doing.
Don't send them a boring plain message. Don't send something you yourself wouldn't have the patience to look at. I'm sure they've already got an abundance of annoying things in their life and don't need your help. Add nice pictures/video. Have as good ASO as possible. For good ASO use keywords that people frequently use when looking for an app like yours. Put them in the app description and possibly in the title. Use sites like AppAny and SearchMan to help you find the right keywords.