Familiarizing oneself with state-of-the-art at the beginning of a PhD
I don't think there is a clear transition between “familiarizing oneself with the subject” and “being an expert in this topic, and generate new ideas and approaches”. The transition is gradual, and it's called “the PhD”.

However, there are ways to quantify this evolution. For example, ask yourself: in a discussion with your advisor and a few other experts on a topic related to your PhD, how able are you to make useful comments and suggestions? How often do you come to your advisor saying “I have tried to do X because I read about it and I think it can apply to my issue”?

Regarding the written “output” of the beginning of a PhD, it pretty much depends on you and your advisor. Mostly, the output is knowledge in your mind, but it can also be useful to make notes (both for yourself and your advisor) on each subtopic you discover. For myself, as an advisor, I ask students to contribute bibliographic notes (written or orally) every now and then, for me and other students of the group who work on related topics.