Strictly speaking from a scientific mindset, the question is unanswerable because it does not seem to be one around which a testable (i.e. falsifiable) theory can be proposed and subjected to experimental testing in an objective manner--that being the nature of the scientific method.

However, scientific knowledge and speculation can be brought to bear in the following two observations. 

First, anything traveling at lightspeed, including of course all photons (and any other massless particles) experience no time in the usual meaning of the term.  Have you noticed that lightspeed particles do not decay? At lightspeed, time stands still for those particles--they cross the universe in the blink of an eye, from the perspective of outside observers.  By this I mean that were they to carry along a clock, and we watch the clock as they travel, we would say that their time stands still.  So in that sense, something does exist "outside of time", at least in the sense we normally think of time.

Second, in the context of the (purely speculative) Many Worlds Interpretation (aka the Multiverse), the universe bifurcates as needed to accommodate alternative outcomes in realities as you propose them, i.e., that "for awhile one exists" then through paradoxical effect no longer has existed--at least in this particular bifurcation of the multiverse.

Okay, I have a headache now so it's time to stop!