I followed these instructions and I made a hello world app with React. I uploaded the development files in my EBS and it worked.
After that I used the command np
I recently deployed my react node based app using the EB CLI. I had to run eb init in my project directory which walks you through setting up the eb config. Here's the steps:
npm init to setup package.json (which you've done)git init to setup a git repoeb init to setup elastic beanstalk settings through its CLIeb deployAWS walks you through these steps assuming you're serving your app with node (which you didn't say, but it's likely).
As a bonus, you might want to setup CI so that AWS builds your app when your tests pass on code push. See the travis yaml file I use to do this.