The basic strategy is this: Post interesting content consistently with relevant hashtags. Use a service like Hashtagify for hashtag ideas. Follow users in your niche and engage with their posts. I also know a couple of people who grew their Instagram accounts quickly solely depending on shoutouts from influencers. You can use a service like ShoutCart for that or contact influencers directly (most of them list their email addresses in their bios).
With drop shipping, you’re effectively partnering with a manufacturer or wholesaler to sell their products. This way, you don’t pay upfront costs to buy inventory, aren’t sitting on unsold items taking up expensive warehouse space, and don’t have to deal with shipping the products yourself. You simply create your site, fill it with drop shippable products, and drive in customers, with almost everything else done for you.