Certainly your past experiences will affect how you perceive the world, process events, think about things, and behave but do you think the high level thinking required for the conception of self needs time or can it be instantaneous? Imagine someone who literally not remember more than 30 seconds ago, so as it were, their life is forever in the current moment. What is their conception of self like? This hypothetical person could still experience qualia such as pain and pleasure, and could still have wishes and plans, but I wonder what about their sense of self -- has anyone ever written about this problem before?
Besides having time continuity in the past, what happens when the sense of self has no future? Imagine you knew that the world was about to end in a few hours. Most people would resort to hedonistic pleasure seeking which I would argue is animalistic in nature and requires no self.
Is the higher level thinking required for the concept of self dependent on forward and backward continuity or could there be such a thing as an 'instantaneous' self?