Yes that's what I believe too, it's not given, it is derived through the inner intuition. And that's why the knowledge of the object, as myself, is subjective rather than objective, as I explained, even though it is knowledge of the object (the subject is the object). We still cannot bypass the medium which is the inner intuition.

So the object is not directly given, it is understood through the temporal order of internal things, just like the outer object is understood through spatial relations. However, I do believe that since the inner intuition is a part of the object to be understood, there actually is an aspect of the object which is given, that's the inner intuition. But the inner intuition is proper to this specific type of object, a subject, and that's why our knowledge of the object (as the subject, oneself) is subjective.

I think Kant makes the distinction between objective and subjective problematic. Both the outer and inner intuitions are needed for the "I" to be sure of its existence. The matter is framed as judgements upon appearances. Kant's disagreement with Hume is that judgement is not only what convinces us as stories and arguments but is constitutional to our ability to experience the world. The "I" appears through that experience and is not known only as an "inner" intuition. Otherwise, Descartes would suffice.

Without the outer, there can be no inner. From that point of view, Kant is demanding an "objective" reference for possibility of the "I". That is how he distinguishes his game from Berkeley's. On the other hand, he has to argue about what is real about time in a sharp departure from Aristotle. That is the issue in the quoted passage.

So, the interesting thing about that for me is how to respect the difference Kant insisted upon.