There is a composer.json and composer.lock file in the repository. All you'd need to do to download all the dependencies is have composer installed and run "composer install".
"application build process" or simply the checkout process? I'd suggest your deployment process shouldn't include a public git repo others can change. Instead, use your own fork on Github, or alternatively host a git repo local to your deploy network. After all, you're trying to avoid dependencies on things like Github working/failing, right? ;-)
I know what you are meant to do is check in your composer.json and composer.lock then do a composer install on the server.
But then you have a external dependency on your install process on live servers, which is a terrible idea. To got around this, I've seen companies say "we have our own package mirror". Or you could just check in the vendor folder?
Another reason I do it: My software package is used by people who aren't PHP programmers and I want them to be able to just grab the files and go with no fuss.
I do appreciate having the vendor folder in git takes space and is a pain ... but I think the trade off is worth it.
I find that it simplifies versioning as well as making it so you don't have to download individual dependencies. What is your suggestion otherwise?