You make proposals related to their software projects. The organization may have multiple projects (that are in scope for GSoC). And the gosc projects are unlikely to affect the whole project, anyway. More often than not, they will be a module, touch a part of a larger project... Note that it is very important to size the project properly, so that it can be done in the allocated time (even with the unexpected that will happen).
As a student you would only need to submit it on the google application, the organization will decide who evaluates it and who would mentor it. Although taking into account what the organization suggests as projects, and engaging with the community earlier to better understand it and their needs go a long way.
I recommend that you look at successful projects from past years to better understand GSoC.
Regards