The question here is really about the self. If, via meditative insight, you come to realize that there is no self, it will then become clear to you that consciousness is not 'my' consciousness, but a universal consciousness that has been sculpted into an illusory and personal view of reality called 'I'. 'I' is the ego, and it wants to go on in perpetuity after death. That is what religion is for; to reinforce the idea of an eternal soul that is the self that must be saved. OTOH, there is the purely materialist view which says 'when you're dead, you're dead!'. (The Buddha, BTW, considered both views to be extreme views, and a view was eventually developed called 'The Middle Path'.) So without a self, and consciousness always present, it must mean that consciousness is already present at birth and after death, as it is not dependent upon the presence of a self, or a brain. Consciousness has been likened to the TV signal, present before the TV set is turned on and after being turned off, or becoming non-functional. But it is more than just signal; it is what actually manifests this material world. Who you really are is what Universal Consciousness is, playing itself as 'I', 'self', and 'soul' named 'Jane/John Doe', this state of personal consciousness being called 'Identification', from which man must awaken to his true nature. This awakening to true Reality in the present moment is what the Middle Path leads to. It is beyond birth and death, and therefore, beyond Time, Space, and Causation.
It is the realization of the individual wave that it is none other than the entire ocean.