Shopify stores are definitely profitable if you have the patience and a decent budget.
The major difference I've seen across high earnings stores and those that close without making a profit is the quality of the products and the shipping times.
Look at this way, would you be willing to spend $40 on a product and wait for it for 14-30 days, without proper tracking? And when it arrives, it is shabbily packed and not that great of a quality? I wouldn't.
If you can keep inventory and check the products' quality before selling them, you can attract a lot more interest from your visitors.
Having said that, if you have a winning product, a product that is high in demand and provides so much value to the customer that they don't mind waiting for it, you've hit gold! You don't need to keep inventory so you've already freed up lots of budget for the Facebook ads.
The second major hurdle would be your marketing plan. If you're planning to go with Facebook ads, you need to have a decent amount of budget set aside for testing your ads. You'll need to test a few ad sets to see what is converting well.
You also need to understand your audience before you spend thousands of dollars on your marketing campaign. There's no better way to burn your money than advertising your product to people who don't care about it.
You also need to make sure that your store looks and feel authoritative. Having a fly-by-night store will not convert as good as a store that looks and feels premium. It should make the checkout process a breeze and the product page (assuming you are sending your traffic to the product page and not the homepage) needs to be properly optimized to capture as many leads as possible.