I have put together a small script to deploy to WPEngine when you use Bedrock and Roots. WPEngine doesn’t support asset building or keeping WordPress in a different directory. The script creates a temporary branch that grabs the packages, dependencies and compiles the assets. It then moves the app folder back to wp-content and removes all other files. The .gitignore files are removed too so the compiled assets are staged. This is then pushed up to staging or production and once completed it’ll remove the branch and you’ll be back on the local working copy.
Feel free to give it a try and hopefully in the future WPE will support the Bedrock workflow.