CLI tools to publish a .sqlproj to database instance

Question

I have a .sqlproj (Microsoft SQL Project) folder (Git repository) which I'd like to Publish to a live database instance using command line tools.

My colleague currently does this manually using Visual Studio:

1. Right-click on Solution then select Rebuild solution
2. Right-click on database project then select Publish
3. Load a profile from a .XML file (containing database connection string and a few other options)
4. Hit Publish to build this database on to the server specified in .XML file

How can I replicate this using command line tools? Preferably I would use Linux, but I'm open to using Windows options too as long as the process is fully automated.

Thanks in advance