So... reality is atemporal?
No, not at all. In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. Since the entire universe passed through (or arbitrarily close to ) the same point at the start of the Big Bang, all clocks are keeping proper time with respect to that event, so it is meaningful to speak of time since the big bang for any point in space time. For events long after the Big Bang and for different observers separated in space, the time interval between events can be different. See this example: http://en.wikipedia.org/wiki/Proper_time#Example_1:_The_twin_.22paradox.22