In the case of sciences, for example, can the birth of a new branch of science be considered as utterly "new"?
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It depends on what you mean by 'can'. Logically, I suppose this is possible. There is no contradiction in saying 'X is a new branch of science and it is utterly new', i.e. without precedent or prefiguration in existing or previously existing science.
Historically and empirically, there are few or no absolute beginnings in science. One science emerges from another. I think this happens in two broadly different ways.
▻ Revolutions in a field of inquiry create new conceptual schemes
Think of physics. There is the physics of Aristotle, then the physics of Ptolemy, then the physics of Copernicus, then the physics of Newton, then of Einstein, then of quantum theory, now of string theory. In each case a conceptual revolution occurred that created in all but name a new science. And each revolution happened because of perceived defects in previous theories.
▻ Progressive refinement
What starts out as a gross, undifferentiated subject matter breaks down into sub-inquiries : in physics, for example, astronomy, dynamics, mechanics, optics, and any number of other fields progressively emerged. New fields of inquiry separated themselves as distinct groups of problems were recognised. But they all developed from existing inquiries.
▻ New combinations
Plainly the intersectional or bridge disciplines such as bio-chemistry, bio-physics, &c. could only emerge from pre-existing sciences.