Believe it or not, things can actually be that simple. You can simply just ask for what you want and get it. It is true that audiences on social media like to follow and like the content of people who are active and that keep them engaged. That being said, you have to learn how to start engaging your audience for you to get those free likes.
You can let your audience feel like they are part and parcel of eth process that goes into making your page what it is. You can ask their opinion on the kind of content that they would like to see, whether they prefer audio or visual content and what they would like to have improved on the page. This is an easier and direct way to get to know exactly what it is that your audience wants thus you will be better placed to get those free likes. If you do not want to take this very direct approach, you can simply choose to start general conversations. Make sure that you keep the conversations going. As you talk more and more with the audience you will get to know them better and get to know what they like.