You don't directly experience a division between subject and object, these are theory-laden terms that are applied in a deliberately directed attention towards distinct ideas; the idea of the objective pole in this particular experience (E) and the idea of its subjective pole are two different ideas, only formally or hypothetically related. They are not experienced simultaneously because you can't experience two different things simultaneously, and they are in fact not strictly related to E, which they only supersede by way of a set of conventional associations, a kind of accepted logic. Also, they are not abstracted out of an original moment in which they occur fused, but an idea of this sort is dictated by that same accepted logic, and so the machinery of association brings up another version of the same ideal split, this time with the monad fusing subject and object, or global noesis and noema, on one side and a deeper avatar of subjectivity called 'awareness' on the other. You can go on with variants of such a schema for a long time. The nature of the mind is that at its best it delights in its skill in playing out the consequences of blindly accepted logics without any ability to question the logics themselves. That creative delight is the very essence of the illusion in which you are held - your best instrument for undoing it is exactly what betrays you.