It's definitely possible to set up a Shopify store in the United States, even if you're in another country. However, you'll need to make sure that you're following all of the legal requirements for selling in the U.S., which may include obtaining a tax ID and following any applicable tax laws. It's best to consult with a legal professional to make sure you're in compliance with all of the necessary regulations. Have you decided on a particular product or niche for your store?
Exciting times setting up your own store! As Idnoble says, you can certain certainly set up a Shopify store in another country as long as you follow all the appropriate requirements. On the shipping/fulfilment side of things, when you're ready, take a look at a shipping app (like Starshipit, for example), which will let you set up the workflows for getting your orders from you to your customers. Happy to share any other advice if you need it!