The concept of Time as the fourth dimension of reality, as featured in the General Theory of Relativity, fits comfortably with the idea of time as a river.
We picture ourselves as 'flowing' through time, moving from point to point along the "Time" dimensional axis. But, the entire axis exists at once--all points at once.
Try to picture a four-dimensional object. If you can do it, you're much smarter than I am. I can, however, picture a four-dimensional object as a three-dimensional object changing in time.
Maybe this is all time is--a construct of our brains, used to incorporate the fourth dimension into our perspective.
In any case, it's theorized that, were you able to travel faster than the speed of light, you'd end up traveling back in time. Even though it is theoretically impossible to exceed the speed of light, this shows that there is a past to travel into. Also, there is a (theoretical) particle, the tachyon, which travels backwards through time. "The Past" must therefore exist. If it exists, it must exist in the state it was in back when I was there. Which means I must still be there, in exactly the same state as when I was back there (which I still am).
So, I exist at every point in my life, simultaneously.
I apologize for the haphazard nature of this writeup.