At work I'm currently modernising a legacy project without composer into an application with less code and thus less bugs. The first composer package I required was an application container to add Dependency Injection to the project. The container I used is called orno/di.
I bootstrapped the container in the index file. After that I registered some basic stuff to it like an object of the Symfony Request class, a Monolog logger with rotating log files, ... Finally I was able to adapt the existing old router to resolve the controllers and their dependencies from the IoC container.
In a couple of hours I had enabled the project to adopt and inject composer loaded classes within minutes.