Can consciousness exist without time? 

From the viewpoint of Advaita Vedanta (and I believe also zen and Dzogchen), time is not just something elusive, but ultimately unreal – only an idea or concept. The same can be said about the concept of ‘now’, which cannot be elucidated or measured in any way. ‘Now’ can only be a symbol of eternity, immeasurable but always present. ‘Eternity’ itself is a symbol or slanted conception of reality or existence/being, which is timeless. For the absolute time does not exist. Consciousness alone is real and, thus, timeless. Stated differently, ‘what is never ceases to be; what is not never comes into being’ (Shankara). Parmenides, Gaudapada, and Shankara were strong in that position.